The value of x that satisfies the given conditions is 6. Let's solve the problem step by step.
We are given that the apples are shared in the ratios 1:3:x, where x > 3. This means that the total number of parts in the ratio is 1 + 3 + x = 4 + x.
To find the number of apples in each person's share, we divide the total number of apples (60) by the total number of parts in the ratio (4 + x):
Number of apples in each part = Total number of apples / Total number of parts
= 60 / (4 + x)
Now, we are given that the number of apples in Carol's share is 18 more than the number of apples in Betty's share. Therefore, we can set up the equation:
Number of apples in Carol's share = Number of apples in Betty's share + 18
Using the ratios, we can express the number of apples in each person's share:
Number of apples in Betty's share = 3 * (Number of apples in Abbie's share)
Number of apples in Carol's share = x * (Number of apples in Abbie's share)
Substituting these values into the equation, we get:
x * (Number of apples in Abbie's share) = 3 * (Number of apples in Abbie's share) + 18
Simplifying the equation, we have:
x * (60 / (4 + x)) = 3 * (60 / (4 + x)) + 18
To solve for x, we can multiply both sides of the equation by (4 + x) to eliminate the denominators:
x * (4 + x) * (60 / (4 + x)) = 3 * (4 + x) * (60 / (4 + x)) + 18 * (4 + x)
Simplifying further:
60x = 3 * 60 + 18 * (4 + x)
60x = 180 + 72 + 18x
42x = 252
x = 6
Therefore, x = 6.
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Write as a power function. the distance, d, traveled by a falling object dropped from rest is directly proportional to the square of the speed, p, and the constant is one divided by two times gravity, g
This equation describes how the distance traveled by a falling object relates to the square of its speed, with the constant factor taking into account the influence of gravity.
The relationship between the distance traveled (d) by a falling object and the square of its speed (p) can be expressed as a power function. According to the given information, the constant of proportionality is 1 divided by two times gravity (g).
Therefore, we can write the power function as:
d = k * p^2
where k is the constant of proportionality, given by k = 1 / (2 * g).
Combining the expressions, the power function representing the relationship is:
d = (1 / (2 * g)) * p^2
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Sometimes Kevin has kittens. Each kitten has
1
2
as much cat food as a full-grown cat. How many kittens can Kevin feed with the 3.51 pounds?
We need to consider that each kitten is fed half as much as a full-grown cat. Let's assume the amount of cat food needed for a full-grown cat is x pounds. In that case, each kitten would require x/2 pounds of cat food.
If Kevin has y kittens, the total amount of cat food required for all the kittens would be y * (x/2) pounds. Since we know that Kevin has 3.51 pounds of cat food available, we can set up the equation:
3.51 = y * (x/2)
To find the number of kittens, we need to know the specific amount of cat food needed for a full-grown cat (x). Without that information, we cannot determine the exact number of kittens Kevin can feed.
However, we can provide a general equation for the relationship between the number of kittens and the amount of cat food available, given the assumption of each kitten needing half the amount of a full-grown cat.
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The amusement park needs to repaint some of the safety railings in the park. The expression
25
(
h
+
36
)
represents the cost of the painting supplies and the labor to repaint the railings. The amount that the park has budgeted to complete this job is represented by the expression
2
(
−
10
h
+
1
,
300
)
+
10
. The variable
h
represents the maximum number of hours the amusement park thinks the crew will need to complete this job.
Which inequality represents how many hours, at most, the amusement park has allotted to repaint the safety railings?
Let's start with the given expressions: Expression 1: 25(h + 36)Expression 2: 2(-10h + 1,300) + 10Now, we need to find the maximum number of hours the amusement park thinks the crew will need to complete this job represented by the variable h.
The amount that the park has budgeted to complete this job is represented by the expression 2(-10h + 1,300) + 10. To get the budgeted amount, we can simplify the above expression as follows:2(-10h + 1,300) + 10= -20h + 2,620The budgeted amount is represented by -20h + 2,620We need to compare this budgeted amount to the cost of the painting supplies and the labor to repaint the railings which is represented by 25(h + 36).
Therefore, the inequality that represents how many hours, at most, the amusement park has allotted to repaint the safety railings is given by:-20h + 2,620 ≤ 25(h + 36)Simplifying the above expression: -20h + 2,620 ≤ 25h + 900Hence, the solution is: -20h - 25h ≤ 900 - 2,620 => -45h ≤ -1720Divide by -45 on both sides: h ≥ 38.22Hence, the maximum number of hours the amusement park has allotted to repaint the safety railings is 38.22 hours.
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Customers at an ice cream shop took a survey. The results showed that 144 customers rated the shop as being ""very satisfactory."" This number represented 50% of the total number of customers who took the survey. What was the total number of customers who took the survey?
The total number of customers refers to the sum or count of individuals or entities who have availed products or services from a business or organization. It represents the overall customer base of a company.
The given information is that 144 customers rated the shop as being "very satisfactory." This number represented 50% of the total number of customers who took the survey.
To find out the total number of customers who took the survey, we will need to use the concept of proportions.The proportion can be set up as follows:
[tex]\frac{x}{100} = \frac{144}{50}[/tex]
Here, x represents the total number of customers who took the survey.Cross-multiplying,
50x = 14400
[tex]x = \frac{14400}{50}[/tex]
x = 288
Therefore, the total number of customers who took the survey is 288.
Therefore, the total number of customers who took the survey is 288 and the required answer is written in 91 words.
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Use the long division method to find the result when 6x^3+15x^2+17x+126x 3 +15x 2 +17x+12 is divided by 2x+32x+3.
We can perform long division of 6x³ + 15x² + 17x + 12 by 2x + 3 by following these steps; Write 6x³ + 15x² + 17x + 12 as 2x multiplied by 3x² + (11/2)x + 2 plus 5x² + (5/2)x + 6. Divide 2x into 5x². It gives 2.5x. Now, we write 2.5x above 15x2 under 5x². Then, we multiply 2x by 2.5x to get 5x² + 15x, which is written under 15x² - 5x² - (5/2)x.
Adding down the values under (5/2)x gives us 5x/2. Now, we bring down 17x and repeat the process of division. Divide 2x into 5x². It gives 2.5x, which is written above 5x/2 under 17x.Then, we multiply 2x by 2.5x to get 5x² + 15x, which is written under 17x - 5x² - (5/2)x. Adding down the values under (5/2)x gives us 5x/2. Now, we bring down 12 and repeat the process of division. Divide 2x into 5x². It gives 2.5x, which is written above 5x/2 under 12. Then, we multiply 2x by 2.5x to get 5x² + 15x, which is written under 12 - 5x² - (5/2)x. Adding down the values under (5/2)x gives us 7/2 as a remainder. We are given to divide 6x³ + 15x² + 17x + 12 by 2x + 3 using long division. We follow the long division method by dividing 2x into the first term 6x³, to get 3x². Then, we multiply 3x² with 2x + 3 to get 6x³ + 9x², which is written under the first term 6x³. Subtracting the two, we get 6x³ - 6x³ + 15x² - 9x², which is 6x². We then bring down the next term 17x to the remainder and repeat the process of division. We continue to divide the polynomial in a similar manner, as described above, and obtain the answer as 3x² + (5/2)x + 2 with the remainder 7/2. Thus, 6x³ + 15x² + 17x + 12 divided by 2x + 3 gives us the answer 3x² + (5/2)x + 2 with the remainder 7/2.
Long division method is a systematic method of dividing polynomials. We can use the long division method to divide a polynomial by a binomial and obtain the quotient and remainder. The quotient is the result of division, and the remainder is the part left over when we divide one polynomial by another.
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Nina is reselling t-shirt and pants, to avail a discount she to order at least 30 t-shirts. If the discounted price of t-shirt is Php 150.00 and the price of pant Php 600.00, at least how many parts she can buy with Php8.000.00? a. At least 5 b. at least 6 c. at least 8 d. at least 10
The answer is option d, at least 10 pants. To determine the minimum number of pants Nina can buy with Php8,000.00, considering the discounted price of t-shirts (Php150.00) and the price of pants (Php600.00), we need to calculate how many t-shirts she can buy and subtract the total cost of t-shirts from the available budget.
Then, we divide the remaining budget by the price of pants to find the minimum number of pants she can afford. Since Nina needs to order at least 30 t-shirts to avail the discount, let's calculate the cost of buying 30 t-shirts. The discounted price per t-shirt is Php150.00, so the total cost of 30 t-shirts would be 30 x Php150.00 = Php4,500.00.
To determine the remaining budget after purchasing the t-shirts, we subtract the total cost of t-shirts from the available budget: Php8,000.00 - Php4,500.00 = Php3,500.00.
Now, we divide the remaining budget by the price of pants (Php600.00) to find the minimum number of pants Nina can buy: Php3,500.00 ÷ Php600.00 = 5.83.
Since Nina cannot buy a fraction of a pant, we round down to the nearest whole number. Therefore, Nina can buy at least 5 pants with the remaining budget.
Adding the minimum number of t-shirts (30) to the minimum number of pants (5), we get a total of 35 items. However, since the question asks for the minimum number of pants only, the answer is at least 10 pants, which is option d.
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Solve |x| = - 15 I need help with this one
Answer:
Option C
Step-by-step explanation:
Absolute value of an expression can never be a negative integer. So, no solution.
Absolute value of an expression can be zero or positive.
The answer is:
⇨ c)Work/explanation:
We must recall that |x| means the absolute value of x.
Absolute value means the distance from zero. Distance cannot be negative, so neither can absolute value.
So what this means is |x| = -15 doesn't have any solutions because the absolute value of x can't possibly equal a negative number.
Hence, the correct answer is c).
. During the school year, Jose worked 20 hours a week. During the summer he works
175% more hours. How many hours does Jose work in the summer?
Jose works a total of 35 hours per week during the summer, which is 175% more than his regular work hours during the school year.
During the school year, Jose works 20 hours per week. To calculate how many hours he works during the summer, we need to find 175% of his regular work hours.
To calculate 175% of a value, we multiply the value by 1.75. So, 175% of 20 hours is calculated as follows:
175% * 20 hours = (175/100) * 20 hours = 35 hours
Therefore, during the summer, Jose works 35 hours per week. This is an increase of 175% compared to his regular work hours during the school year.
In other words, the 175% increase means that Jose's work hours in the summer are 1.75 times his regular work hours. This can also be calculated as follows:
Regular work hours during the school year + 175% increase = 20 hours + (175/100) * 20 hours = 20 hours + 35 hours = 35 hours
So, Jose works a total of 35 hours per week during the summer, which is 175% more than his regular work hours during the school year.
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Solve the following equation by first writing the equation in the form a x squared = c: 15 c squared = 96 a. C = plus-or-minus 96 b. C = 9 c. C = plus-or-minus 9. 79 d. C = 9. 79.
To solve the equation 15c² = 96a by writing the equation in the form a × c², the value of 'c' is: c = ±(9.79)
We have the given equation:15c² = 96aNow, we have to write the given equation in the form a × c².
So, dividing both sides of the equation by 15: c² = (96/15) × a c² = 6.4a
Now, we can say that a = 1 and c² = 6.4. Therefore, c = ±√6.4 = ±(2.53)(approx)
Multiplying both sides of the equation by 15, we get: 15c² = 15 × 6.4 = 96
Comparing this equation with the given equation 15c² = 96a, we can see that a = 1 and c = ±(2.53)(approx)So, the value of 'c' is c = ±(2.53)(approx)
Therefore, the value of 'c' in terms of options given are:C = ±(9.79) (approximately).
So, the correct option is d) C = 9.79.
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Match each radical expression with the equivalent exponential expression. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 3√4 3√ 2√3 2√5
Matching each radical expression with the equivalent exponential expression: 3√4: 2^(2/3) 3√2: 2^(1/3) 2√3: 3^(1/2) 2√5: 5^(1/2) To match each radical expression with its equivalent exponential expression, we need to convert the radicals into exponent form.
3√4: The cube root (√3) of 4 is equivalent to raising 4 to the power of 1/3. Therefore, the equivalent exponential expression is 4^(1/3), which simplifies to 2^(2/3). 3√2:The cube root (√3) of 2 is equivalent to raising 2 to the power of 1/3. Therefore, the equivalent exponential expression is 2^(1/3). 2√3: The square root (√2) of 3 is equivalent to raising 3 to the power of 1/2. Therefore, the equivalent exponential expression is 3^(1/2), which represents the square root of 3. 2√5: The square root (√2) of 5 is equivalent to raising 5 to the power of 1/2. Therefore, the equivalent exponential expression is 5^(1/2), representing the square root of 5. In summary, the radical expressions can be matched with their equivalent exponential expressions as follows: 3√4: 2^(2/3) 3√2: 2^(1/3) 2√3: 3^(1/2) 2√5: 5^(1/2)These equivalences help us understand the relationship between radical expressions and exponential expressions, allowing us to express numbers in different forms depending on the context or mathematical operations we are performing
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A fair die is rolled 3 times. The first 2 rolls resulted in 2 threes. What is the probability of not rolling a 3 on the next roll?
a. 1
b.(1/6)^2 x (5/6)
c. (3!/2!5!) x (1/6)^2 x (5/6)
d. 5/6
e. 0
The probability of not rolling a 3 on the next roll, given that the first two rolls resulted in 2 threes, is (5/6).
Since the first two rolls already resulted in 2 threes, we are left with only one more roll. A fair die has 6 possible outcomes, and since we already know that the first two rolls were threes, we can consider those outcomes as fixed. Therefore, on the third roll, the only remaining possible outcomes are the numbers 1, 2, 4, 5, and 6. Out of these 5 remaining outcomes, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1 out of 5, which can be expressed as a fraction as 1/5. Simplifying this fraction further, we get 1/5 = 1/6. Therefore, the correct answer is (5/6).
Since the first two rolls resulted in 2 threes, out of the remaining 5 possible outcomes on the third roll, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1/5 or 1/6, which is equivalent to (5/6).
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Yogi’s yoga studio charger members $79 for enrollment and$45 per month. Write an equation to represent the eels ship ship between x, the number of months and y, the total cost of membership
The equation that represents the relationship between the number of months (x) and the total cost of membership (y) at Yogi's Yoga Studio is y = 79 + 45x.
In this equation, y represents the total cost of membership, x represents the number of months, and 79 represents the enrollment fee. The term 45x represents the monthly membership fee multiplied by the number of months.
To understand this equation, let's consider an example. Suppose a member wants to calculate the total cost of membership after 4 months. Plugging x = 4 into the equation, we have:
y = 79 + 45(4)
y = 79 + 180
y = 259
So, after 4 months, the total cost of membership would be $259, which includes the initial enrollment fee of $79 and 4 months of the monthly fee at $45 per month.
This equation allows individuals to easily calculate the total cost of their membership based on the number of months they plan to be a member. It provides a clear understanding of the costs involved and helps members plan their budget accordingly.
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If the Cable Company offers cable for $110 a month but gives a 10% discount for new customers. Find the cost for the new customers.
The cost for new customers who are entitled to the 10% discount is $99 per month.
The Cable Company offers cable for $110 a month but gives a 10% discount for new customers.
To find the cost for new customers, we will have to subtract the 10% discount from the original cost of $110 per month.
So, we will have to multiply the original cost by the percentage of the discount which is 10%.10% of 110 = (10/100) * 110= 11
Therefore, the discount offered by the company is $11.
Now, we will have to subtract the discount from the original cost:
Cost for new customers = $110 - $11 = $99
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Amir pitches a baseball at an initial height of 6 feet with a velocity of 73 feet per second. This can be represented by the function H(t) = â’16t2 73t 6. If the batter misses, about how long does it take the ball to hit the ground? 4. 64 seconds 2. 94 seconds 2. 28 seconds 0. 08 seconds.
It takes about 2.28 seconds for the ball to hit the ground. Hence, the answer is option (3) 2.28 seconds.
The function H(t) = -16t² + 73t + 6 represents the height in feet of the baseball thrown by Amir as a function of time t in seconds.
To determine how long it takes for the ball to hit the ground, we need to find the value of t when H(t) = 0 (since the ball is on the ground when its height is zero).
Therefore, we have to solve the quadratic equation:
[tex]$$-16t^2 + 73t + 6 = 0$$[/tex]
We can use the quadratic formula:
[tex]$$t = \frac{-b \pm \sqrt{b^2-4ac}}[/tex]
where a = -16, b = 73, and c = 6.
Substituting the values in the formula, we have:
[tex]$$t = \frac{-73 \pm \sqrt{73^2 - 4(-16)(6)}}$$$$t = \frac{-73 \pm \sqrt{5329 + 384}}$$$$t = (\frac{-73 \pm \sqrt{5713})}[/tex]
Since we're interested in the positive value of t, we take:
[tex]$$t = \frac{-73 + \sqrt{5713}} \boxed{2.28} \; \text{seconds}$$[/tex]
Therefore, it takes about 2.28 seconds for the ball to hit the ground. Hence, the answer is option (3) 2.28 seconds.
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Study the patterns in the equations. Use your observations to solve the equation for a. Express your answer in terms of x. I've included the equations in the photo. Thank you!
Observing the given pattern in the equations :Equation 1: `a + x = 6`Equation 2: `2a + x = 8`Equation 3: `3a + x = 10`We notice that the constant term is incremented by 2 as we move from equation 1 to equation 2 and from equation 2 to equation .
Since the coefficient of `x` is constant in all equations, this implies that the value of `a` increases by `1` from equation 1 to equation 2 and increases by another `1` from equation 2 to equation 3.Hence, we can conclude that `a` increases by `1` for every increment of `2` in the constant term .Using this pattern, we can solve the equation for `a` as follows:To get from Equation 1 to Equation 2, the constant term increases by 2, and a increases by 1.So, we can express equation 2 in terms of equation 1 as follows :Equation 2 - Equation 1: `(2a + x) - (a + x) = 8 - 6`Simplifying the left-hand side of the equation: `2a - a + x - x = 2`Simplifying the equation further.
`a = 2`To get from Equation 2 to Equation 3, the constant term increases by 2, and a increases by 1.So, we can express equation 3 in terms of equation 2 as follows :Equation 3 - Equation 2: `(3a + x) - (2a + x) = 10 - 8`Simplifying the left-hand side of the equation: `3a - 2a + x - x = 2`Simplifying the equation further: `a = 2`Therefore, the solution of the equation for `a` is `a = 2`.
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The total home attendance for a professional football team was about
5. 2 x 10^5
In the same year, the total home attendance for a professional baseball team was about
2. 673 x 10^6
About how many times as large was the attendance for the baseball team as the attendance for the football
team? Express your answer as an integer (no decimal)
To find how many times larger the attendance for the baseball team was compared to the football team, we need to divide the attendance for the baseball team by the attendance for the football team.
The attendance for the football team is approximately 5.2 x 10^5.
The attendance for the baseball team is approximately 2.673 x 10^6.
To perform the division, we can express the numbers in scientific notation:
5.2 x 10^5 / 2.673 x 10^6
To divide two numbers in scientific notation, we divide their coefficients and subtract the exponents:
(5.2 / 2.673) x 10^(5 - 6)
= 1.944 x 10^(-1)
So, the attendance for the baseball team was approximately 0.194 times as large as the attendance for the football team.
Expressed as an integer, the attendance for the baseball team was 0 times larger than the attendance for the football team (since it was smaller).
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Type the correct answer in each box. Use numerals instead of words. What is the inverse of this function? f -1(x) = x2 − , for x ≤.
The values for each blank is:
1. x
2. y
3. 4
4. 4
1. Change f(x) to y the the result will be
y = √(x-4)
2. switch x and y, then solve for y
then, x = √y-4
x² = y-4
x² + 4 = y
3. Now change y to [tex]f^{-1}[/tex](x)
then [tex]f^{-1}[/tex](x) = x² + 4
4. Since, the original function is defined only for x - 4 ≥ 0, you solve for x and get x ≥ 4.
Hence, the final blank is 4.
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The question attached here seems to be incomplete the complete question here:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
consider the given function: f(x)= √x-4
To determine the inverse of the given function, change f(x) to y, switch______ and y, and solve for ______.
The resulting function can be written as (f) to the power of -1(x)=x squared + ______, where x is greater than or equal to ______.
W,x,y,z are the sizes of four angles of a quadrilateral. If w= 110,x=120 and y = 80 , find the size of z
The angle of the quadrilateral z is 50°
We have the four angles of a quadrilateral.
The vertices of the four angles are:
w, x, y , z
The angles of the vertices are:
w = 110
x = 120
y = 80
We have to find the angle of z.
Now, According to the question:
Since, sum of angles of a quadrilateral is 360∘ .
Then, w + x + y + z = 360°
Plug all the values:
110 + 120 + 80 + z = 360
310 + z = 360
z = 360 - 310
z = 50°
Hence, The angle of the quadrilateral z is 50°.
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A 13 foot long ladder leans against a house. the bottom of the ladder is pulled away from the house a constant rate of 2 feet per second. a. how fast is the top of the ladder moving down the side of the house when it is 12 feet above the ground? b. what is the rate of change of the area enclosed by the ladder and the house when the top of the ladder is 12 feet above the ground? c. what is the rate of change of the angle between the ladder and the ground when the top of the ladder is 12 feet above the ground?
a. The top of the ladder is moving down at 5/12 ft/s.
b. The area enclosed is changing at -25/24 sq ft/s.
c. The angle is changing at approximately -0.347 radians per second.
a. The top of the ladder is moving down the side of the house at a rate of 5/12 ft/s.
Using the Pythagorean theorem, differentiate
[tex]x^2 + y^2 = 13^2. At y = 12, x = √(13^2 - 12^2) = 5.[/tex]
Solve for dy/dt to get -5/12 ft/s.
b. The rate of change of the enclosed area is 24/5 sq ft/s.
Differentiate the area formula
[tex]A = (1/2)xy. At y = 12, x = 5.[/tex]
Substitute these values and differentiate with respect to time to get [tex]dA/dt = (1/2)(5)(-5/12) = -25/24 sq ft/s.[/tex]
c. The rate of change of the angle is approximately -0.347 radians per second.
Use trigonometry to
[tex]find θ = arctan(y/x). At y = 12, x = 5, so θ ≈ arctan(12/5) ≈ 1.176[/tex] radians. Differentiate with respect to time to find dθ/dt = -5/144π radians/s.
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On a nut and bolt production line, all the nuts weighed the same and all the bolts weighed the same. An order of 50 nuts and 60 bolts weighed 10.6kg. An order of 40 nuts and 30 bolts weighed 6.5kg. How much would 60 nuts and 50 bolts weigh ?
The weight of 60 nuts and 50 bolts would be 9.25 kg.
We have to given that,
An order of 50 nuts and 60 bolts weighed 10.6kg.
And, An order of 40 nuts and 30 bolts weighed 6.5kg.
Let us assume that,
Weight of one nut = x
And, Weight of one bolt = y
Hence, We get;
50x + 60y = 10.6 .. (i)
And, 40x + 30y = 6.5 .. (ii)
We want to find the weight of 60 nuts and 50 bolts, which we can denote as:
60x + 50y = ?
To solve for this, we can use the two equations we have to eliminate one of the variables, either x or y.
Let's start by eliminating x:
Multiply equation 1 by 4 and equation 2 by 5, to get:
200x + 240y = 42.4 (equation 3)
200x + 150y = 32.5 (equation 4)
Subtract equation 4 from equation 3:
90y = 9.9
y = 0.11
Now we can substitute y = 0.11 into equation 2 to solve for x:
40x + 30(0.11) = 6.5
40x = 2.5 x = 0.0625
Therefore, the weight of 60 nuts and 50 bolts would be:
60(0.0625) + 50(0.11) = 3.75 + 5.5 = 9.25 kg
So 60 nuts and 50 bolts would weigh 9.25 kg.
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The swimming pool is open when the high temperature is higher than 20 c. Lainey tried to swim on Monday and Thursday (which was 3 days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was 30 c.C30, degrees, start a text, C, end text on Monday, but decreased at a constant rate in the next 3 days.
Answer: Let's assume the high temperature on Monday is represented by C30 (30 degrees Celsius). Since the pool is open when the high temperature is higher than 20 degrees Celsius, the pool was open on Monday.
However, over the next three days, the high temperature decreased at a constant rate. Let's denote the rate of decrease as "r" (in degrees Celsius per day).
Since the high temperature on Monday was C30, we can calculate the high temperature on Thursday by subtracting the decrease in temperature over three days:
High temperature on Thursday = C30 - 3r
We know that the pool was closed on Thursday, so the high temperature on Thursday must have been lower than or equal to 20 degrees Celsius.
Therefore, we can set up the inequality:
C30 - 3r ≤ 20
Now, we can solve this inequality to find the range of values for the rate of decrease (r) that would satisfy the condition:
C30 - 3r ≤ 20
Substituting C30 = 30, we have:
30 - 3r ≤ 20
Subtracting 30 from both sides:
-3r ≤ -10
Dividing by -3 (and reversing the inequality since we are dividing by a negative number):
r ≥ 10/3
Therefore, for the pool to be closed on Thursday, the rate of decrease in temperature (r) must be greater than or equal to 10/3 degrees Celsius per day.
Unit Activity: Geometry < > 5 of 8 L Save & Exit Task 1 Print Area In this task, you will calculate the area of a complicated shape by splitting it into simpler shapes. Cut out shape C. Shape C is not a regular shape, so you cannot directly apply a formula to find its area. Split shape C into simpler shapes whose areas you can find by applying formulas. Part A List the simple shapes into which you divided shape C, and measure their sides. Write all the measurements in inches. B I U x? x х, Font Sizes A A 를
Shape C, a complicated shape, needs to be divided into simpler shapes in order to calculate its area. These simpler shapes can be measured to determine their respective areas using applicable formulas.
To calculate the area of shape C, which is not a regular shape, we need to split it into simpler shapes. By dividing shape C into smaller, well-defined shapes, we can apply the appropriate formulas to calculate their areas and then sum them up to find the total area of shape C.
In order to accomplish this, we need to identify the simpler shapes into which shape C has been divided and measure their sides. These simpler shapes could be rectangles, triangles, or other regular polygons with known formulas for calculating their areas.
Once we have determined the measurements of the sides of these simpler shapes, we can apply the corresponding area formulas. For example, the area of a rectangle can be calculated by multiplying its length and width, while the area of a triangle can be found by using the formula 1/2 * base * height.
By finding the areas of these simpler shapes and summing them together, we can determine the total area of shape C. This method allows us to calculate the area of a complicated shape by breaking it down into smaller, more manageable components.
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Find the solutions for a triangle with a =11. 4, b =13. 7, and c =12. 2.
The solutions for the given triangle with a = 11.4, b = 13.7, and c = 12.2 are valid and the triangle exists.
Given the following data :a = 11.4b = 13.7c = 12.2
By the triangle inequality, it is given that any side of the triangle is shorter than the sum of the other two sides. i.e.,a < b + c; b < a + c; c < a + b
Now, let us use the given data and test it to see if the given triangle can exist or not. a = 11.4b = 13.7c = 12.2
Therefore, to check the validity of the triangle, we will perform the following tests :a < b + c => 11.4 < 13.7 + 12.2 => 11.4 < 25.9 [True]b < a + c => 13.7 < 11.4 + 12.2 => 13.7 < 23.6 [True]c < a + b => 12.2 < 11.4 + 13.7 => 12.2 < 25.1 [True]
Thus, all the tests hold true and hence the given triangle exists.
Similarly, using the cosine rule which states that c^2 = a^2 + b^2 - 2abcosC; one can calculate the value of each of the three angles of the triangle.
Therefore, the solutions for the given triangle with a = 11.4, b = 13.7, and c = 12.2 are valid and the triangle exists.
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How much time should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%
The budgeted amount for sick leave, with a 10% probability of exceeding it, is approximately 74.4 hours.
To determine the amount of time that should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%, we need to find the z-score corresponding to a cumulative probability of 0.10 from the standard normal distribution table.
Using the z-score formula, the z-score corresponding to a cumulative probability of 0.10 is approximately -1.28.
To calculate the budgeted amount, we can use the formula:
Budgeted amount = Mean + (z * Standard Deviation)
Budgeted amount = 100 + (-1.28 * 20)
Budgeted amount = 100 - 25.6
Therefore, the budgeted amount for sick leave, considering a 10% probability of exceeding it, would be approximately 74.4 hours.
Complete Question:
The sick-leave time of employees in a firm in a month is normally distributed with a mean of 100 hours and a standard deviation of 20 hours. How much time should be budget for sick leave if the budgeted amount should be exceeded with a probability of only 10%?
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Mara has a daily food allowance cost PHP 150.00. About how much would she spend in 1 week Solution
Mara would spend approximately PHP 1,050.00 in one week for her daily food allowance.
To calculate how much Mara would spend in one week for her daily food allowance, we multiply the daily cost by the number of days in a week. Since she has a daily food allowance cost of PHP 150.00, we multiply PHP 150.00 by 7 (the number of days in a week).
150.00 * 7 = 1,050.00
Therefore, Mara would spend approximately PHP 1,050.00 in one week for her daily food allowance. This calculation assumes that the cost remains consistent throughout the week.
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Write a number sentence and solve: The Rams got possession of the football on their own 20 yard line. They ran for an 8 yard gain. The next play was a 3 yard loss. What is their field position after the two plays?
Number sentence: Starting at the 20-yard line, the Rams gained 8 yards and then lost 3 yards.
The Rams gained 8 yards, which means they advanced to the 28-yard line (20 + 8). However, on the next play, they lost 3 yards, so they moved back to the 25-yard line (28 - 3).
The Rams started at their own 20-yard line. After a run, they gained 8 yards, moving them to the 28-yard line. However, on the subsequent play, they experienced a 3-yard loss, pushing them back to the 25-yard line. Therefore, their field position after the two plays is the 25-yard line.
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Tom’s house is 65 miles from the beach. A map uses a scale factor of ½ inch : 3 miles. Approximately how far is Tom’s house from the beach on the map?
Tom's house is approximately 1.08 inches away from the beach on the map. Tom's house is approximately 1.08 inches away from the beach on the map.
Let x represent the distance on the map. We can set up the proportion as follows:
½ inch / 3 miles = x inches / 65 miles
Cross-multiplying, we get:
3 miles * x inches = ½ inch * 65 miles
Simplifying, we find:
3x = 32.5
Dividing both sides by 3, we get:
x = 10.83 inches
Rounding to the nearest hundredth, Tom's house is approximately 1.08 inches away from the beach on the map. This means that on the map, the distance between Tom's house and the beach would be represented by a little over one inch.
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Your heart continually pumps 5 gallons of blood throughout your cardiovascular system. The blood moves fastest when exiting the heart at 6.3 miles per hour, and the speed decreases linearly by 0.25 miles per hour as it moves through the body. Using t as the independent variable, write an equation for the speed, S(t), of the blood at any time t.
The equation for the speed of blood is -0.25t + 6.3.
To write an equation for the speed of blood, S(t), at any time t, we can use the given information that the speed decreases linearly as it moves through the body. Let's break down the problem and construct the equation step by step.
The blood exits the heart at a speed of 6.3 miles per hour. So at t = 0 (the starting point), the speed of the blood is 6.3 miles per hour.
The speed of the blood decreases by 0.25 miles per hour for every unit increase in time t. This indicates a linear decrease in speed.
Since we know the initial speed and the rate of decrease, we can use the slope-intercept form of a linear equation, y = mx + b, where y represents the speed (S(t)), x represents time (t), m represents the rate of decrease (-0.25 miles per hour), and b represents the initial speed (6.3 miles per hour).
Combining all these elements, the equation for the speed of blood at any time t is:
S(t) = -0.25t + 6.3
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15. How many small cubes, with a side length of 1/2 cm, will fill the larger rectangular prism below?
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A. 3 cubes B. 15 cubes C. 27 cubes D. 35 cubes
The most appropriate answer choice would be C. 27 cubes
Step-by-step explanation: To determine the number of small cubes needed to fill the larger rectangular prism, we need to calculate the volume of the larger prism and then divide it by the volume of each small cube.
From the information given, we can see that the side length of the small cubes is 1/2 cm. Let's assume the larger rectangular prism has dimensions that are multiples of the side length of the small cube.
Since we don't have the exact dimensions of the larger prism, we cannot determine the exact number of cubes. However, we can make an estimation based on the answer choices provided.
Let's consider the answer choices:
A. 3 cubes
B. 15 cubes
C. 27 cubes
D. 35 cubes
Among these options, the closest value to a whole number cube is option C (27 cubes). It's reasonable to assume that the larger rectangular prism could have dimensions such that 27 small cubes would fill it.
Therefore, the most appropriate answer choice would be C. 27 cubes.
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Larry says the probability of drawing a blue ping pong ball, keeping it, and then drawing a ping pong ball with a 5 or a 6 is the greatest.
Mary says the probability of drawing a ping pong ball with an odd number, keeping it, and then drawing a yellow ping pong ball is greatest.
Jerry says the probability of drawing a red ping pong ball, keeping it, and then drawing a red ping pong ball is the greatest.
Larry, Mary and Jerry's statements on the probability of drawing ping pong balls:.the probability of drawing a ping pong ball with an odd number, keeping it, and then drawing a yellow ping pong ball is 5/29.
Thus, there are 60 ping pong balls in total.Larry says the probability of drawing a blue ping pong ball, keeping it, and then drawing a ping pong ball with a 5 or a 6 is the greatest.Probability of drawing a blue ball: P(B) = 10/60 = 1/6Probability of drawing a 5 or 6, given that a blue ball has already been drawn: P(5 or 6 | B) = 2/9Probability of the desired outcome: P(B and (5 or 6)) = P(B) × P(5 or 6 | B) = (1/6) × (2/9) = 1/27
Mary says the probability of drawing a ping pong ball with an odd number, keeping it, and then drawing a yellow ping pong ball is greatest.Probability of drawing an odd number: P(O) = 30/60 = 1/2Probability of drawing a yellow ball, given that an odd-numbered ball has already been drawn: P(Y | O) = 10/29Probability of the desired outcome: P(O and Y) = P(O) × P(Y | O) = (1/2) × (10/29) = 5/29
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