The total number of books completed by 2:45 pm will be 42.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that when the librarian starts downloading new books at 11:00 am, there are 15 already loaded. When she checks at noon, there are 25 books completely loaded.
The number of books loaded in 1 hour is calculated as,
N = 25 - 15
N = 10 books
Now from 12 noon to 2:45 pm, the time in hours will be,
T = 165 minutes or 165 / 60 = 2.75 hours
The equation for the number of books loaded will be written as,
y = 15 + 10T
y = 15 + ( 10 x 2.75)
y = 15 + 27.5
y = 42.5 or 42
The completely loaded books are 42 in number.
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how much less is the value including 13% VAT in Rs.3200 than Rs.3820
The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."
Here, we have VAT.
A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.
Value on Rs. 3200 with 13% VAT
= 3200 + 30% of 3200
= 3200 + 960
= 4160 rupees
Now, the less value,
= 4160 - 3820
= 340 rupees.
Therefore, the less value is 340 rupees.
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Solve for y in this diagram. Justify your answer.
The value of y in the isosceles triangle is AC = 6 cm
What Is an Isosceles Triangle?
A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ABC
Now , the angle ∠ABC = 25°
The angle ∠ACB = 25°
So , the 2 angles of a triangle is 25° so , the third angle is 130°
So , the triangle is an isosceles triangle
And , the two sides of the triangle is AB = AC
The measure of side AB = 6 cm
The measure of side AC = measure of side AB
Therefore , the measure of side AC = 6cm
Therefore , the value of AC is 6 cm
Hence , the measure of side AC of triangle is 6 cm
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the average iq test scores of an srs of 31 seventh-grade girls in a midwest school district is 105.84. suppose that the standard deviation of iq scores in this population is known to be 15. iq scores in a broad population are supposed to have mean of 100. is there evidence that the mean in this district di ers from 100? use signi cance level
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
X = 89 represent the mean of seventh-grade girls in Midwest school district
s = 15 represent the standard deviation for the sample
n = 31 sample size
μ = 100 represent the value that we want to test
'a' represent the significance level for the hypothesis test.
't' would represent the statistic (variable of interest)
[tex]p_{v}[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses,
We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:
Null hypothesis: μ = 100
Alternative hypothesis: μ ≠ 100
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
t = (X-μ) / ([tex]\frac{s}{\sqrt{n} }[/tex] ) (Equation-1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
t = [tex]\frac{89-100}{\frac{15}{\sqrt{31} } }[/tex]
t = -4.08
Calculate the P-value
First we need to calculate the degrees of freedom given by:
[tex]df = n-1[/tex]
[tex]df = 31 -1[/tex]
[tex]df = 30[/tex]
Since is a two tailed test the p value would be:
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 )
[tex]p_{v}[/tex] = 0.00031
Therefore,
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
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in a class of 40 students, 20 have examination scores below 77% and 20 have scores above 77%. which measure(s) of central tendency can you immediately determine?
Observing the information provided and using concept of central tendency parameters of statistics, The central tendency which we can immediately determine is median.
What is statistics?A field of mathematics that deals with gathering, analyzing, interpreting, and presenting vast amounts of numerical data.
What do you mean by measure of central tendency?The statistical test that determines whether a single result accurately represents a whole distribution is known as measure of central tendency.
total students = 40.
half = 20 students.
20 have scores below 77% and 20 have above 77%.
Thus, We can immediately determine that the median of score is 77%.
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Bob is a member of a gym. He paid a joining fee, plus a monthly fee. The equation below represents the amount he has paid as a function of the number of
months he has been a member of the gym. Interpret the slope of the function in terms of the problem.
y=22m +39
A. Bob pays $39 for 22 months.
B. Bob pays $22 per year.
C. Bob pays $22 per month
D. Bob pays $39 per month
Bob pays $22 per month as 39 is joining fee which is only for first month
What is an example of a slope intercept form?
Slope-Intercept Form Examples
Example 1: Assuming a line has a slope of 1/2 and intersects the y-axis at (0, -3). Find the line's equation. Y = x/2 - 3 is the solution to the line's equation. Example 2: Using the horizontal line slope intercept formula, determine the equation at which the y-axis intersects (0, 8).
How is a slope equation solved?
Write the equation of the line in slope-intercept form to determine the slope from the equation. Utilize inverse procedures to find y, then write it as y=mx+b. Since the slope is the x variable's coefficient, or the number before x, you can thus readily see the slope.
Given that:
y=22m+39
Slope of the function is 22 and it is membership fee of a month .
If bob wants to increase membership for a months , he has to pay 22 extra and joining fee of 39
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Which parent function is represented by the graph?
O A. An exponential parent function
• B. The quadratic parent function
• C. The absolute value parent function
O D. The linear parent function
Parent function is represented by the graph is
B. The quadratic parent function
What is Parent function?
A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.
A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.
The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.
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alyssa has $75 less than three times eric together they have $905 how much money do they each have
Alyssa has the money of worth $660
Eric has the money of worth $245
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the amount Alyssa has.
Let y be the amount Eric has.
alyssa has $75 less than three times eric
=> x= 3y - 75
Together they have $905
=> x + y =905
Substitute x
=> 3y - 75 +y = 905
4y = 905 +75 = 980
y = 980 /4 = 245
x= 3y - 75 = 3(245) - 75 = 660
Alyssa has $660
Eric has $245
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what is the correct congruence statement for triangles shown
Answer:
It is NLJ
Step-by-step explanation:
Trust me lol
Explain Harvey's error in the following scenario.
Harvey's sow has just delivered five piglets. The veterinarian has examined the mother and babies, the
piglets have nursed, and it is time for everyone to get some rest. Harvey has filled the pen with clean, dry
straw, and he puts all the pigs in the pen to spend their first night together.
Harvey's mistake in this scenario is that he put the pigs on a bed of straw that could infect their belly buttons. Additionally, he did not ensure that they consume colostrum in the first hours of life.
How should we treat a newborn pig?When we have a pregnant sow and we have to manage the postpartum procedure, we must make sure of different necessary procedures so that the piglets are well and their lives are not at risk in the following hours or days.
Among the procedures necessary for the piglets to be well are breathing, feeding and hygiene. In detail, once the piglet is extracted from its mother, we must make sure that it is breathing correctly. Secondly, we must clean it properly and make sure that its navel is completely clean to avoid infections. Finally we must give colostrum as food within the following hours after birth.
Additionally, we must place it in a clean place where it is not exposed to possible bacteria or infections, so the option of putting it on a bed of straw would be ruled out due to hygiene for the pig.
According to the above, Harvey's mistake was that he did not clean the piglets when they were born, did not give them colostrum, and put them on straw. Actually, he made three mistakes.
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The area of the caribbean sea is 2.7182 × 106 km2. the area of the south atlantic ocean is 4.027 × 107 km2. find the total area. write the final answer in scientific notation with the correct number of significant digits. 4.29882 × 108 km2 4.299 × 107 km2 3.75518 × 1013 km2 3.755 × 1013 km2
The total area of the Caribbean sea and the South Atlantic ocean is 4.299 × 10⁷ km². The correct option is the second option 4.299 × 10⁷ km²
Calculating total areaFrom the question, we are to determine the total area of the water bodies.
From the given information
"The area of the Caribbean sea is 2.7182 × 10⁶ km²"
and
"The area of the South Atlantic ocean is 4.027 × 10⁷ km²"
To determine the total area, we will add up the two areas
Total area = 2.7182 × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10¹ × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10⁷ km² + 4.027 × 10⁷ km²
Total area = 4.29882 × 10⁷ km²
Total area ≈ 4.299 × 10⁷ km²
Hence, the total area is 4.299 × 10⁷ km²
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Answer:
Hence, the total area is 4.299 × 10⁷ km²
Step-by-step explanation:
Which equation represents a hyperbola with a center at (0,0) a vertex at (-48,0) and a focus at (50,0)
The equation of hyperbola will be;
⇒ x²/48² - y²/14² = 1
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
In hyperbola,
The value of center = (0, 0)
The value of vertex = (- 48, 0)
The value of focus = (50, 0)
Now,
We know that;
The equation of hyperbola is,
⇒ (x - h)²/a² - (x - k)²/b² = 1
Where, (h, k) is center, (h ± a, k) is the vertex.
Here, The value of center = (0, 0)
The value of vertex = (- 48, 0)
The value of focus = (50, 0)
So, h = 0, k = 0
a = 48, c = 50
We get;
⇒ (x - 0)² / 48² - (y - 0)² / b² = 1
⇒ x² / 48² - y² / b² = 1
Since, c = √a² + b²
⇒ b = √c² - a²
⇒ b = √50² - (-48)²
⇒ b = √196
⇒ b = 14
Hence, We get;
⇒ x² / 48² - y² / b² = 1
⇒ x² / 48² - y² / 14² = 1
Thus, The equation of hyperbola is;
⇒ x²/48² - y²/14² = 1
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20 newspapers in 4 piles = newspapers per pile
Answer: 5
Step-by-step explanation:
20/4 = 5
Find the amount with the same value as:
70 x 7-2
A
0
B
14
C
149
D
17
The value of the numerical expression 70 / (7 - 2) will be 14. Then the correct option is B.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numerical expression is given below.
⇒ 70 / (7 - 2)
Simplify the expression, then we have
⇒ 70 / (7 - 2)
⇒ 70 / 5
⇒ 14
The worth of the mathematical articulation 70/(7 - 2) will be 14. Then the right choice is B.
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The correct expression is given below.
70 / (7 - 2)
Find the number that makes the ratio equivalent to 6:1.
?:10
Answer:
60
Step-by-step explanation:
?=60, multiply each side of the ratio by 10 to get the answer
6×10:1×10
60:10
A car traveled at an average speed of 60 mph for two hours. how far did it travel? responses 30 miles 30 miles 60 miles 60 miles 120 miles 120 miles 150 miles
Answer: 120 miles
Step-by-step explanation:
If a car goes 60 miles per hour then in two hours (60×2) it will go 120
at the city museum, child admission is $5.30 and adult admission is $9.80. on thursday, 143 tickets were sold for a total sales of $1149.40. how many adult tickets were sold that day?
The number of adult tickets which were sold that day as calculated from the given data is 29.
First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.
To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.
This is represented by the following equation,
$8.90A + $5.30C = $928
Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:
3 * C = A
Now we can answer our first problem by substituting 3 * C for A.
8.9 (3C) + 5.3C = 928
26.7C + 5.3C = 928
32C = 928
C = 29
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1 point
Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and
221 hot dogs for $2.35 each. Which calculation will give the closest estimate of the sales
of soft drinks and hot dogs?
The calculation that will give the closest estimate of the sales of soft drinks and hot dogs is 360 * 2 + 220 * 2
How to determine the calculation that will give the closest estimateFrom the question, we have the following parameters that can be used in our computation:
Time = one week
Number of cans = 362
Unit price of soft drink = $1.75
Number of hot dogs = 221
Unit price of hot dogs = $2.35
The calculation that will give the closest estimate is represented as
Estimate = Number of cans * Unit price of soft drink + Number of hot dogs * Unit price of hot dogs
Substitute the known values in the above equation, so, we have the following representation
Estimate = 362 * 1.75 + 221 *2.35
Approximate
Estimate = 360 * 2 + 220 * 2
Hence, the expression is 360 * 2 + 220 * 2
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Question 1 (1 point)
How many solutions does the system of equations have?
Answer: 0
Step-by-step explanation: The reasoning behind this is that both functions will never intersect which would mean there are no solutions for the system equation.
What is the simplest form of (x^2+5x-6) / (x^2+9x+18)?
a) (x+2) / (x+6)
b) 1/3
c) (x-1) / (x+3)
d) -1/3
Answer:
a. [tex]\frac{x+2}{x+6}[/tex]
Step-by-step explanation:
[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]
Rewrite one eighteenthx3y + seven eighteenthsxy2 using a common factor.
one thirdxy(6x2 + 7y)
one thirdx2y(6x2 + 9y)
one eighteenthxy(x2 + 7y)
one eighteenthx3y2(y + 7)
Answer:
C
Step-by-step explanation:
1/18 x³y + 7/18 xy²
1/18 xy (x² + 7y)
7
10
1
2/5
Cedric has
3
of the pie
of the pie
of the pie
of the nie
4
of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
C
PR
The fraction of the pie left that each friend will receive is; 3/8 of the pie
How to divide fractions?Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.
The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.
For example, 3/8 divided by 3/4 would be;
3/8 divided by 3/4 = 3/8 * 4/3
Now, we are told that cedric has 3/4 of a pie left.
Now, he wants to share equally among two of his friends, it means that;
Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8
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Complete question is;
Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
a dark eyed man marries a dark eyed woman, but they have a blue eyed child. what is the probability that their second child will have blue eyes?
The probability that their second child will have blue eyes is 1/4.
Here dark eye is dominant trait and blue eyes is recessive trait.
So both man and woman is heterozygous dominant and the blue eye child is homozygous recessive.
Man and woman will produce four types of genotypes in children. One homozygous dominant (dark eye), one homozygous recessive (blue eye) and two heterozygous dominant (dark eye).
So the probability of any child to be blue eyed (homozygous recessive) will be 1/4.
Hence we get the required answer.
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7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
[tex]xvertex = -b / 2a[/tex]
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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the owners of a supermarket chain are looking into the effectiveness of the supermarket's loyalty card program. specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. chloe works in the marketing department of the chain and is assigned to answer the owners' inquiry. she randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. what are the null and alternative hypotheses for this hypothesis test?
The null and different hypotheses for hypothesis test are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
Null hypotheses
Null hypothesis is usually what researchers or scientists try and confute, and if the null hypothesis is accepted, we have a tendency should modification our opinion, i.e., we have a tendency should modification our original opinion or statement so as to match the null hypothesis. H0 denotes the null hypothesis.Given that:
sample size (η)= 196
sample proposition (p^) = 114/196
Let p denote the population proportion of people who use a loyalty card.
The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]
Hence, the null and alternative hypothesis are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
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fillings how much do prices vary for filling a cavity? to find out, an insurance company randomly selects 10 dental practices in california and asks for the cash (non-insurance) price for this procedure at each practice. the interquartile range is $74.
The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.
1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.
2. The insurance company then computes the interquartile range of the prices for each practice.
3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.
The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.
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write a logarithmic equation (using only real numbers) that has no real solutions. explain why there are no real solutions.
The equation is log_2 (3x - 5) = 9 There are no real solutions to this equation because the logarithm of a negative number is undefined. The left side of the equation would require the argument to be negative, thus making the equation impossible to solve.
This equation cannot be solved because the logarithm of a negative number is undefined. The left side of the equation is of the form log_2 (N), where N is some real number.For the equation to have any real solutions, N needs to be greater than 0. However, in this equation, N is equal to 3x - 5, which can be negative for certain values of x. This means that there is no real number x that can be substituted into the equation to make it true, since the logarithm of a negative number is not defined. Therefore, this equation has no real solutions.
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Which ordered pair is a solution to the equation y = –23x + 9?
A (−32,10)
B (0,10)
C (−1,1023)
D (23,10)
Answer: None of these
Step-by-step explanation:
A. If [tex]x=-32[/tex], then [tex]y=745[/tex], not [tex]10[/tex].
B. If [tex]x=0[/tex], then [tex]y=9[/tex], not [tex]10[/tex].
C. If [tex]x=-1[/tex], then [tex]y=32[/tex], not [tex]1023[/tex].
D. If [tex]x=23[/tex], then [tex]y=-520[/tex], not [tex]10[/tex].
The video game club lost 8 members which was 28% of their group.
What was the original attendance of the video game club?
HELP!!!
The original attendance of the video game club was 28.57 members.
To determine the original attendance of the video game club, you can use the following formula:
Original attendance = (Number of members lost) / (Percent of group that left)
Plugging in the values from the problem, we get:
Original attendance = (8 members) / (28%)
To solve this equation, you need to convert the percent to a decimal by dividing it by 100. This gives us:
Original attendance = (8 members) / (0.28)
Then, you can solve the equation by dividing the number of members lost by the decimal equivalent of the percent:
Original attendance = 28.57 members
Therefore, the video gaming club had 28.57 members when it first started.
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What is the approximate value of y − x? 4.9° 6.2° 11.1° 17.2°
Answer:
Step-by-step explanation:
11.1
The approximate value of y - x is 17.2°.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given a right triangle LMN.
Using the tangent function,
tan (y) = 19.1 / 14.1
= 1.3546
y = tan⁻¹ (1.3546) = 53.56°
We know that,
x + y = 90°, since the other angle is 90°.
x = 90 - 53.56° = 36.44°
y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°
Hence the value of y - x is 17.2°.
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A worker in a silver mine descends 26 feet use an integer to represent the change in the workers position
Answer: -26 feet
Step-by-step explanation:
