Answer: 24kg
Step-by-step explanation:
Ratio given:
Dog = 3 (Weight of cat)
Substitute the (Weight of cat) with the given unit:
Dog = 3(8kg)
Multiply
Dog = 24kg
Use the diagram shown. Lines p and q are parallel.
How many degrees is the measure of ∠4?
Answer:
61°
Step-by-step explanation:
∠4 is the vertical angle to the 61° angle. This means they will have the same measure, so ∠4 is 61°.
Will tracks the high and low tempters in his town for five days during a cold spell in January his results are shown in the table below
Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.
Define change in temperaturecalculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.
Change in temperature on Monday from High to low
=15-10=5°F
Change in temperature on Tuesday from High to low
=8-(-4)=12°F
Change in temperature on Wednesday from High to low
=-2-(-5)=3°F
Change in temperature on Thursday from High to low
=-3-(-7)=4°F
Change in temperature on Friday from High to low
=-1-(-12)=11° F
Days when change in temperature more than 10° F are Tuesday and Friday.
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The Complete question is attached below:
Pls help There is a 20% chance that a customer walking into a store will make a purchase. A computer was used to generate 5 sets of random numbers from 0 to 9, where the numbers 0 and 1 represent a customer who walks in and makes a purchase.
A two column table with title Customer Purchases is shown. The first column is labeled Trial and the second column is labeled Numbers Generated.
What is the experimental probability that at least one of the first three customers that walks into the store will make a purchase?
A) 60%
B) 13%
C) 40%
D) 22%
The experimental probability that at least one of the first three customers that walks into the store will make a purchase is 60%.
What is experimental probability?It is determined by counting the number of times an event occurs in a given experiment and dividing the total number of trials by the number of successful outcomes.
The experimental probability that at least one of the first three customers that walks into the store will make a purchase is calculated by dividing the total number of customers who make a purchase by the total number of customers who enter the store.
In this case, there are 3 trials and 2 customers who make a purchase.
The experimental probability is 3 by 5 which is the total number of trials.
Thus, the experimental probability
=3/5
= 60%.
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On the day a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. Assume the
number of viewers continues to double each day.
1. On which day will 640 people see the video? Explain or show your reasoning.
2. What strategy would you use to find the first day when more than 20,000 people will see the video (if the trend continues)?
On the 7th day after the videο was pοsted, 640 peοple will see the videο.
What is Statistics?Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data.
1 Let's start by finding the pattern in the number οf viewers. We knοw that οn the first day, 5 peοple watched the videο. On the next day, the number οf viewers dοubled tο 5 x 2 = 10. On the third day, the number οf viewers dοubled again tο 10 x 2 = 20. We can see that the number οf viewers is dοubling each day, which means we can write the number οf viewers as:
[tex]V = 5 x 2^n[/tex]
where n is the number οf days after the videο was pοsted.
Nοw we want tο find οn which day the number οf viewers will be 640. Sο we can set V equal tο 640 and sοlve fοr n:
[tex]640 = 5 x 2^n[/tex]
[tex]2^n = 128[/tex]
n = lοg2(128) = 7
2. Tο find the first day when mοre than 20,000 peοple will see the videο, we can set V equal tο 20,000 and sοlve fοr n:
[tex]20,000 = 5 x 2^n[/tex]
2^n = 4,000
n = lοg2(4,000) ≈ 11.29
Since n represents the number οf days after the videο was pοsted, we can rοund up tο the next whοle number tο find the first day when mοre than 20,000 peοple will see the videο. Therefοre, οn the 12th day after the videο was pοsted, mοre than 20,000 peοple will see the videο if the trend cοntinues
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in nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
The correct option is (C). In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: ΔY = f(x₁ + ΔX₁, X₂ + ΔX₂, ..., Xk + ΔXk) - f(x₁, X₂, ..., Xk)
where ΔX₁, ΔX₂, ..., ΔXk are the changes in the respective explanatory variables. This equation represents the change in Y due to a simultaneous change in all the explanatory variables by ΔX₁, ΔX₂, ..., ΔXk. Option (C) represents the same equation in a slightly different notation. Option (A) only considers one explanatory variable, and option (B) does not include the baseline value of the function. Therefore, option (C) is the correct answer.
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Complete question:
In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
A. ΔY= f(x₁ +Xq, X2, Xx) = f(Xq, X2....XK). 1 1'
B. ΔY = F(X,+ ΔX₁₁ X2, Xx) - F(X₁₁ X2, Xk). ---
C. ΔY = f(x,+ ΔX₁₁ X₂ + ΔX2, Xx+ ΔX x) - F(X₁₁ X2, Xx). 1°
D. ΔY = f(x₁ +Xq, X2, Xk).
7. Complete the comparison: 17>?
O A. 18
O B. 17
O C. 39
O D. 1
O Mark for review will be highligh
Answer: 39
39 is the only answer option greater than 17
Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formula.
In response to the stated question, we may state that Therefore, the trigonometry exact values of sin(u), cos(u), sin(2u), and cos(2u) are 4/5, 3/5, 24/25, and -7/25, respectively. The exact value of sin(t/2) is 2√5 / 5.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
Using the given triangle, we can find the values of sin(u), cos(u), and tan(u) as follows:
sin(u) = opposite / hypotenuse = 4 / 5
cos(u) = adjacent / hypotenuse = 3 / 5
tan(u) = opposite / adjacent = 4 / 3
To find the values of sin(2u) and cos(2u), we can use the double angle formulas:
[tex]sin(2u) = 2 sin(u) cos(u)\\cos(2u) = cos^2(u) - sin^2(u)\\sin(2u) = 2 (4/5) (3/5) = 24/25\\cos(2u) = (3/5)^2 - (4/5)^2 = -7/25[/tex]
sin(t/2) = ± [tex]\sqrt((1 - cos(t)) / 2)[/tex]
We need to determine the sign of the square root based on the quadrant in which t/2 lies. Since 7t/2 is in the second quadrant (between pi and 3pi/2), t/2 is in the second quadrant as well (between pi/2 and pi). In the second quadrant, sine is positive and cosine is negative. Therefore, we take the positive square root:
[tex]sin(t/2) = \sqrt((1 - cos(t)) / 2)\\= \sqrt((1 - (-3/5)) / 2)\\= \sqrt(8/10)\\= \sqrt(4/5)\\[/tex]
= 2/√5
= 2√5 / 5
Therefore, the exact values of sin(u), cos(u), sin(2u), and cos(2u) are 4/5, 3/5, 24/25, and -7/25, respectively. The exact value of sin(t/2) is 2√5 / 5.
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Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = e−8/√n lim n→[infinity] an =
The sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex], is convergent sequence because the limit of an exists, that is as n approaches infinity, so the sequence an approaches 1 ( finite value).
The sequence can be convergent if the limit is zero, or if the limit is finite. The divergent sequence is one whose limit is not finite. The limit can be found suing the limit properties or by simplification method, as applicable. We have, an sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex]. We have to check whether the sequence converges or diverges. Using limits, [tex]lim_ {n->\infty } a_n = lim_{n-> oo} e^{\frac{-8}{\sqrt{n}}} [/tex]
n approaches infinity, so square root of n approaches infinity,
= e⁻⁰
= 1/e⁰ = 1 ( finite )
Therefore, it is a convergent sequence.
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Mrs. Cabana has 8 pets total. Three of the pets are chameleons and the rest are fish. Select all the answers that are a ratio relationship for Mrs. Cabana's pets.
Question 1 options:
Multi choice
3/5
3 to 11
3:8
5 to 8
8:1
Answer: numbers 1,3 and 4
Step-by-step explanation:
Individuals who identify as male and female were surveyed regarding their diets.
Vegetarian
Pescatarian
Total
89
101
190
Male
Female
Total
Meat-eater
35
37
72
12
23
35
24
14
38
Vegan
18
27
45
What is the probability that a randomly selected person is a meat-eater? Round your
answer to the hundredths place.
Answer:
To find the probability that a randomly selected person is a meat-eater, we need to add up the number of meat-eaters and divide by the total number of individuals surveyed. From the given table, we can see that there are 72 meat-eaters out of a total of 190 individuals surveyed:
Total meat-eater = 72
Total surveyed = 190
So the probability of selecting a meat-eater is:
P(meat-eater) = Total meat-eater / Total surveyed
P(meat-eater) = 72 / 190
P(meat-eater) = 0.38 (rounded to the hundredths place)
Therefore, the probability that a randomly selected person is a meat-eater is 0.38 or 38%.
P, Q, R, S, T and U are different digits.
PQR + STU = 407
Step-by-step explanation:
There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:
P = 2
Q = 5
R = 1
S = 8
T = 9
U = 9
With these values, we have:
PQR = 251
STU = 156
And the sum of PQR and STU is indeed 407.
Venell put together a model train with 25 train cars. Each train car is 80 millimeters long. How many meters long is Venell's model train if there are no gaps between cars? (1 meter = 1,000 millimeters)
Answer: 2 meters
Step-by-step explanation:
The length of one train car is 80 millimeters. Therefore, the length of the entire train is:
25 cars × 80 mm per car = 2000 mm
To convert millimeters to meters, we need to divide by 1000:
2000 mm ÷ 1000 = 2 meters
Therefore, Venell's model train is 2 meters long.
I will mark you brainiest!
What is the length of EF?
A) 2.4
B) 3.8
C) 0.5
D) 1.2
Answer:
the answer is 2.4 for ef
pls mark me brainliest
Tell me which brand or which size is a better buy.
Answer:
The answer is brand B
Step-by-step explanation:
You divide $14.88 by 24 which equals 68 cents per item.
Then brand B is 60 cents per item which is the better buy!
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45 pounds each, and the small boxes weigh 35 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4925 pounds in boxes, how many of each type of box is it carrying?
The required number of boxes that the truck contain is 70 small boxes and 55 large boxes.
What is simplification?In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
Given that, Number of large boxes weigh 45 pounds each, and the small boxes weigh 35 pounds each. There are 125 boxes in all, the truck is carrying a total of 4925 pounds
Let the number of large boxes will be l and the number of small boxed be s,
According to the question,
l + s = 125
l = 125 - s - - - - - (1)
Again,
45l + 35s = 4925
put 1 in the above equation,
45[125 - s] + 35s = 4925
5625 - 45s + 35s = 4925
10s = 700
s = 70
Now,
l = 125 - 70
l = 55
Thus, the required number of boxes that the truck contain is 70 small boxes and 55 large boxes.
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If the triangles above are reflections of each other, then BC ≅ to:
A) DE.
B) ED.
C) EF.
D) DF.
E) AC.
Answer:
D
Step-by-step explanation:
If their reflections are congruent to each other then looking at the diagram we can see a reflection just like a mirror where its flipped on the other side of the dotted line. When flipping it and aligning one triangle to the other we find that BC is congruent to DF
find two positive numbers that satisfy the given requirements. the sum of the first and twice the secind is 100 and the product is a maximum
Answer: The two positive numbers that satisfy the given requirements are 25 and 50.
Step-by-step explanation:
Let's call the two positive numbers x and y. We want to maximize their product while satisfying the condition that "the sum of the first and twice the second is 100", or mathematically:
x + 2y = 100
We can use algebra to solve for one of the variables in terms of the other:
x = 100 - 2y
Now we want to maximize the product xy:
xy = x(100 - 2y) = 100x - 2xy
Substituting x = 100 - 2y:
xy = (100 - 2y)y = 100y - 2y^2
To find the maximum value of this expression, we can take the derivative with respect to y and set it equal to zero:
d(xy)/dy = 100 - 4y = 0
Solving for y gives:
y = 25
Substituting y = 25 into the equation x + 2y = 100, we get:
x + 2(25) = 100
x = 50
Therefore, the two positive numbers that satisfy the given requirements are x = 50 and y = 25, and their product is:
xy = 50(25) = 1250
Kingsley knows that 1inch is about 2.45 centimeters. He wants to write an equation he can use to convert any given length in inches (i) to centimeters (c)
How should Kingsley write his equation?
A.) c/i = 2.54
B.) c = 2.54i
C.) i = c/2.54
Since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
What is equation ?
An equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). The expressions on either side of the equals sign may contain one or more variables, which are unknown values that can be determined by solving the equation.
Kingsley wants to convert a given length in inches to centimeters. He knows that 1 inch is about 2.45 centimeters.
Let's call the length in inches "i" and the length in centimeters "c".
We want to find an equation that relates i and c. We know that 1 inch is about 2.45 centimeters, so we can write:
1 inch = 2.45 centimeters
To convert from inches to centimeters, we can multiply the length in inches by 2.45. So:
c = 2.45i
This is the equation Kingsley can use to convert any given length in inches to centimeters.
Alternatively, we can rearrange this equation to solve for i:
c = 2.45i
Divide both sides by 2.45:
c/2.45 = i
So the equation for converting from centimeters to inches is:
i = c/2.45
Therefore, since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
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write a quadratic function in standard form that passes through the points (-8,0) ,(-5, -3) , and (-2,0) .
F(x)=
A quadratic function in standard form that passes through the points [tex](-8,0), (-5,-3), and (-2,0)[/tex] is equals to the [tex]f(x) = (1/3)( x^{2} + 10x + 16)[/tex].
What are some examples of quadratic functions?f(x) = ax2 + bx + c, in which a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.
How do you determine whether an equation is quadratic?In other terms, you have a quadratic equation if a times the squares of the expression after b plus b twice that same equation not square plus c equals 0.
[tex]f(x) = ax^{2} + bx + c ----(1)[/tex]
is determined by three points and must be [tex]a[/tex] not equal [tex]0[/tex]. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs [tex](-8,0), (-5,-3)[/tex], and [tex](-2,0)[/tex] and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point[tex]( -8,0), x = -8, y = f(x) = 0[/tex] in equation [tex](1)[/tex],
[tex]= > 0 = a(-8)^{2} + b(-8) + c[/tex]
[tex]= > 64a - 8b + c = 0 -------(2)[/tex]
Similarly, for second point [tex]( -5,-3) , f(x) = -3, x = -5[/tex]
[tex]= > - 3 = a(-5)^{2} + (-5)b + c[/tex]
[tex]= > 25a - 5b + c = -3 --(3)[/tex]
Continue for third point [tex](-2,0)[/tex]
[tex]= > 0 = a(-2)^{2} + b(-2) + c[/tex]
[tex]= > 4a -2b + c = 0 --(4)[/tex]
So, we have three equations and three values to determine.
Subtract equation [tex](4)[/tex] from [tex](2)[/tex]
[tex]= > 64 a - 8b + c - 4a + 2b -c = 0[/tex]
[tex]= > 60a - 6b = 0[/tex]
[tex]= > 10a - b = 0 --(5)[/tex]
subtract equation [tex](4)[/tex] from [tex](3)[/tex]
[tex]= > 21a - 3b = -3 --(6)[/tex]
from equation (4) and (5),
[tex]= > 3( 10a - b) - 21a + 3b = -(- 3)[/tex]
[tex]= > 30a - 3b - 21a + 3b = 3[/tex]
[tex]= > 9a = 3[/tex]
[tex]= > a = 1/3[/tex]
from [tex](5)[/tex] , [tex]b = 10a = 10/3[/tex]
from [tex](4)[/tex], [tex]c = 2b - 4a = 20/3 - 4/3 = 16/3[/tex]
So,[tex]f(x)= (1/3)( x^{2} + 10x + 16)[/tex]
Hence, required values are [tex]1/3, 10/3,[/tex] and [tex]16/3[/tex].
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Answer:
f(x) = (1/3)x² + (10/3)x + 16/3-------------------------------------
Given 3 points of a quadratic function and two of them lie on the x-axis:
(-8, 0) and (-2, 0)These two points are representing the roots of the function. With known roots we can show the function in the factor form:
f(x) = a(x - x₁)(x - x₂), where a - coefficient, x₁ and x₂ are rootsSubstitute the roots into the equation and use the third point with coordinates x = - 5, f(x) = - 3, find the value of a:
-3 = a(- 5 + 8)((-5 + 2)- 3 = a(3)(-3)3a = 1a = 1/3This gives us the function in the factor form:
f(x) = (1/3)(x + 8)(x + 2)Convert this into standard form of f(x) = ax² + bx + c:
f(x) = (1/3)(x + 8)(x + 2)f(x) = (1/3)(x² + 10x + 16)f(x) = (1/3)x² + (10/3)x + 16/3Let f be the function given by f(x) = e-2x2.
a) Find the first four nonzero terms and the general termof the power series for f(x) about x = 0.
b) Find the interval of convergence of the power series forf(x) about x = 0. Show the analysis that leads to yourconclusion.
c) Let g be the function given by the sum of the first fournonzero terms of the power series for f(x) about x = 0. Show thatabsolute value(f(x) - g(x)) < 0.02 for -0.6<= x <=0.6.
a) The first four nonzero terms of the power series for f(x) about x=0 are
e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!
The general term of the power series is (-2)^n (2x)^(2n) / (2n)!
b) The interval of convergence of the power series is (-∞, ∞).
c) To estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series, we can use the Lagrange form of the remainder
|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!
a) To find the power series for f(x) about x = 0, we can use the Maclaurin series formula
f(x) = Σ[n=0 to ∞] (fⁿ(0)/n!) xⁿ
where fⁿ(0) denotes the nth derivative of f evaluated at x=0.
In this case, we have
f(x) = e^6(-2x^2)
fⁿ(x) = dⁿ/dxⁿ(e^6(-2x^2)) = (-2)^n(2x)^ne^6(-2x^2)
So, we can write the power series as
f(x) = Σ[n=0 to ∞] ((-2)^n(2x)^n e^6(0))/n!)
= Σ[n=0 to ∞] ((-2)^n (2x)^n /n!)
To find the first four nonzero terms, we substitute n = 0, 1, 2, and 3 into the above formula
f(0) = e^6
f'(0) = 0
f''(0) = 24
f'''(0) = 0
So, the first four nonzero terms of the power series are:
e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!
The general term of the power series is
(-2)^n (2x)^(2n) / (2n)!
b) To find the interval of convergence of the power series, we can use the ratio test
lim [n→∞] |((-2)^(n+1) (2x)^(2n+2) / (2n+2)! ) / ((-2)^n (2x)^(2n) / (2n)!)|
= lim [n→∞] |-4x^2/(2n+1)(2n+2)|
= lim [n→∞] 4x^2/(2n+1)(2n+2)
Since this limit depends on the value of x, we need to consider two cases
i) If x = 0, then the power series reduces to the constant term e^6, and the interval of convergence is just x=0.
ii) If x ≠ 0, then the series converges absolutely if and only if the limit is less than 1 in absolute value
|4x^2/(2n+1)(2n+2)| < 1
This is true for all values of x as long as n is sufficiently large. So, the interval of convergence is the entire real line (-∞, ∞).
c) We can use the Lagrange form of the remainder to estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series
|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!
where M is an upper bound for the fifth derivative of f(x) on the interval [-0.6, 0.6].
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Y=3x-4 4x+3y=1 what does X and y equal?
Answer:
{y,x}={-1,1}
to leave and take
How many degrees are in 5/8 of a circle
Answer:
225 degrees
Step-by-step explanation:
It is: 5/8 of 360 = 225 degrees.
5/8 of a circle is equivalent to 225 degrees.
Given,
5/8 of a circle.
Now,
A full circle represents 360 degrees .
So,
1 complete circle = 360 degrees
Let 5/8 of a circle represents x degrees,
1 complete circle = 360 degrees
5/8 of circle = x degrees
Cross multiply,
x = 5/8 * 360
x = 225 degrees.
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The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble??
A) 11
B) 33
C) 32
D) 22
The number οf times that Greg chοοses a yellοw pebble is 22 times.
Thus, option D is correct.
Finding the number οf chοices:Tο find the number οf pοssible chοices, calculate the number οf chances in the tοtal number οf οutcοmes.
Since we need tο find the number οf chοices that are expecting a yellοw pebble, find the tοtal number οf yellοw pebbles in the number οf pebbles in bοth Claire and Laura's cases and find the tοtal number οf yellοw pebbles.
Here we have
A table belοw shοws the number οf painted pebbles by Claire and Laura
Frοm the table,
Number οf pebbles that Laura painted = 8 yellοw, 7 green, 10 blue
Number οf pebbles that Claire painted = 14 yellοw, 5 green, 6 blue
Tοtal number οf yellοw pebbles = 8 + 14 = 22
Given that
Greg chοοses a pebble at randοm frοm the bοx 75 times, and each time replaces the pebble
Hence, the number οf time that Greg get yellοw pebble = number οf yellοw pebbles
Therefοre, The number οf times that Greg chοοses a yellοw pebble is 22 times.
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Need help answering all 3 of these please anyone
a. The slope of AB is [tex]m = 1[/tex] and slope of BC is [tex]m = -4/7.[/tex]
b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.
c. The mid-point of Diagonal AC is [tex](0, -1/2)[/tex]
What are the Quadrilaterals?A clοsed shape nοted fοr having sides with variοus widths and lengths is a quadrilateral. It is a clοsed, two-dimensional pοlygοn with fοur sides, fοur angles, and fοur vertices. Quadrilaterals include the trapezium, parallelοgram, rectangle, square, rhοmbus, and kite, amοng οthers.
a.
Slope is given by
[tex]A = (-2, 3) and B = (-5, 0)[/tex]
[tex]m = 1[/tex]
[tex]B = (-5, 0) and C = (2, -4)[/tex]
[tex]m = -4/7[/tex]
Thus, The slope of AB is m = 1 and slope of BC is [tex]m = -4/7[/tex] .
b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.
c. Midpoint of a segment is given by the 2 divided by of sum x and and sum of y
Thus, Diagonal [tex]A = (-2, 3)[/tex] and [tex]C = (2, -4)[/tex]
Midpoint [tex]= ((-2 + 2), (3 + -4))[/tex]
[tex]= ((0), (-1))[/tex]
Now divide them by 2
[tex]= ((0/2), (-1/2))[/tex]
[tex]= (0, -1/2)[/tex]
Therefore, the mid-point of Diagonal [tex]AC is (0, -1/2)[/tex]
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Asaad invests $6800 in two different accounts. The first account paid 14 %, the second account paid 11 % in interest. At the end of the first year he had earned $856 in interest. How much was in each account?
Answer:
Step-by-step explanation:
Let x be the amount invested in the first account, which pays 14% interest. Then the amount invested in the second account, which pays 11% interest, is 6800 - x.
The interest earned on the first account is 0.14x, and the interest earned on the second account is 0.11(6800 - x). The total interest earned is the sum of these two amounts, so we have:
0.14x + 0.11(6800 - x) = 856
Simplifying and solving for x, we get:
0.14x + 748 - 0.11x = 856
0.03x = 108
x = 3600
Therefore, Asaad invested $3600 in the first account and $3200 (6800 - 3600) in the second account.
A pyrotechnician is running a test for a fireworks display he is providing for an event downtown. He launches a test shell from the top of a tower. The elevation, in meters, of the test shell t seconds after being projected is shown by the following expression.
Look at the picture attached and then choose your answer pls!
Select the best description of the term 29.4 in the expression.
A. the total time the test shell is in the air
B. the initial velocity of the test shell
C. the highest elevation the test shell reaches
D. the initial elevation of the test shell
The best description of that term 29.4 in the expression is the initial velocity of the test shell. That is option B.
Who is a pyrotechnician?A pyrotechnician is defined as the individual that has been trained for safe storage, handling, and functioning of pyrotechnics such as fireworks.
While testing the display of the fireworks, he took note of the following:
The elevation in meters
The time in seconds
The change in velocity should be noted as the velocity of distance covered by a moving object with time.
Therefore, the term 29.4 is the initial velocity of the fireworks he projected.
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What quadratic function is represented by the graph?
A. f(x) = −2x²+x+6
B. f(x) = 2x²x+6
C. f(x) = 2x²+x+6
D. f(x) = − 2x² - x - 6
Answer:
Answer: C. f(x) = 2x²+x+6
In a certain company, employees contribute to a welfare fund at the rate of 4% of the first $1000 earned, 3% of the next $1000, 2% of the next $1000 and 1% of any extra monies. How much will an employee who earned $20,000 contribute to the fund?
The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.
An employee who earned $20,000 will contribute $260 to the welfare fund.
To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.
The first $1000 will have a contribution rate of 4%.
Contribution for the first $1000 = 4% of $1000 = $40.
The next $1000 will have a contribution rate of 3%.
Contribution for the next $1000 = 3% of $1000 = $30.
The next $1000 will have a contribution rate of 2%.
Contribution for the next $1000 = 2% of $1000 = $20.
The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.
Contribution for the remaining amount = 1% of $17,000 = $170.
Now, let's sum up the contributions for each tier:
$40 + $30 + $20 + $170 = $260.
Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.
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If F1 = 4y - 6, F2 = 9y + 3 and F3 = -y - 8, simplify F1 × F2 - F3 in terms of y.
Answer:
To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.
F1 × F2 can be expanded using the distributive property:
F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3
= 36y^2 + 12y - 54y - 18
= 36y^2 - 42y - 18
Now we can subtract F3 from the result:
F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)
= 36y^2 - 42y - 18 + y + 8
= 36y^2 - 41y - 10
Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.
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graph each system of equations. solve each system and clearly mark the solutions on your graph. assume 0\le \theta \le 2\pi : r
The system of equation is now written as:
y = −2x−8
y = x+ 1
First, we will plotting two system of equations on the same axis, and then we'll explore the different factors to consider when plotting two linear inequalities on the same axis. The technique for drawing a system of linear equations is the same as for drawing a single linear equation. We can draw two lines on the same axis system using an array of values, slope and y-intercept or x-y-intercept.
Now,
these using slope-intercept form on the same set of axes. Remember that slope-intercept form looks like
y = mx+ b, so we will want to solve both equations for y.
First, solve for y in 2x+y=−8
2x+ y = −8
OR, y = −2x− 8
Second, solve for y in
x− y = −1
Or, y = x+1
The system is now written as
y = -2x - 8
y = x + 1
Now you can plot the two equations using their slope and intercept on the same set of axes as shown in the figure below. Note that these charts have one thing in common. It is their intersection, the point that lies on the two lines. In the next section we will verify that this point is the solution of the system.
Complete Question:
Graph each system of equations. Solve each system and clearly mark the solutions on your graph and consider the following system of linear equations in two variables.
2x+ y = −8 and x− y = −1
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