The total value of the prize is $936,000.
The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.
What is the total value of the prize?The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:
= $900/week x 52 weeks/year x 20 years
= $936,000.
How much money is needed to put into the account?We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r
Plugging in the values:
PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154
PV = $900 x 657.221075423
PV = $591,498.968.
Read more about state lotto
brainly.com/question/28988219
#SPJ1
A pendulum on a grandfather clock is swinging back and forth and it keeps time. A device measures the height of the pendulum above the floor as it swings back and forth. At the beginning of the measurements, the pendulum is at its highest point, 36 cm above the floor. After 4 seconds, it is at its lowest point, 12 cm above the floor. At 8 seconds, the pendulum is back at its greatest height from the floor. Assume that the graph of the distance above the floor varies sinusoidally as time. A table of values is given below.
b. Write an equation of the form H(t)=A cos (Bt) +D for your graph above.
c. What is the distance (to the nearest tenth) from the floor when t=6.5 seconds?
The distance from the floor when t = 6.5 seconds is about 13.7 cm.
We are given that;
H(t)=A cos (Bt) +D
Now,
b. To write an equation of the form H(t) = A cos (Bt) + D for the graph, we need to find the values of A, B, and D.
A is the amplitude of the cosine function, which is half the difference between the maximum and minimum values of H(t). In this case, the maximum value is 36 and the minimum value is 12, so:
A = (36 - 12) / 2 A = 12
D is the vertical shift of the cosine function, which is the average of the maximum and minimum values of H(t). In this case:
D = (36 + 12) / 2 D = 24
B is related to the period of the cosine function, which is the time it takes for one complete cycle. In this case, the period is 8 seconds, because H(t) repeats its values every 8 seconds. The formula for B is:
B = 2π / period
So:
B = 2π / 8 B = π / 4
Therefore, the equation is:
H(t) = 12 cos (π/4 t) + 24
c. To find the distance from the floor when t = 6.5 seconds, we need to plug in t = 6.5 into the equation and evaluate H(t). Using a calculator, we get:
H(6.5) = 12 cos (π/4 × 6.5) + 24 H(6.5) ≈ 13.7
Therefore, by the equation answer will be 13.7 cm.
To learn more about equations :
brainly.com/question/16763389
#SPJ1
Examine the figure of two parallel lines cut by a transversal.
One interior angle has a measure of 75 degrees; the alternate interior angle has a measure of 4 x plus 7 degrees.
What is the value of x?
The value of x is 17.
Given that, two parallel lines cut by a transversal, forming one interior angle has a measure of 75 degrees; the alternate interior angle has a measure of 4x + 7 degrees.
Since, we know that, the alternate interior angles between parallel lines are equal so,
4x+7 = 75
4x = 68
x = 17
Hence the value of x is 17.
Learn more about alternate interior angles click;
https://brainly.com/question/28795639
#SPJ1
Which type of fax funds military defense
The correct option is A which is federal tax.
The type of tax that funds military defence in the United States is the federal income tax. This is a tax levied by the federal government on individuals, businesses, and other entities based on their income. A portion of this tax revenue is allocated towards funding the military, including salaries for personnel, equipment, and operations.
It's important to note that not all of the federal income tax revenue is earmarked for military defence. The federal government uses this revenue to fund a variety of programs and services, including healthcare, education, infrastructure, and more. The allocation of funds towards military defence is determined by Congress and can vary from year to year based on national security needs.
Other taxes, such as state income tax, local income tax, and FICA tax (which funds Social Security and Medicare), do not directly fund military defence. However, all taxpayers contribute to the national defence in some way, as the federal government relies on a variety of revenue sources to fund its operations and programs, including military defence.
To know more about federal tax follow
https://brainly.com/question/12217635
#SPJ1
NEED HELP ASAP PLS AND THX PIC IS ATTACHED
The trigonometric ratios for angle a are given as follows:
[tex]\sin{a} = \frac{3}{\sqrt{13}}[/tex][tex]\cos{a} = \frac{2}{\sqrt{13}}[/tex]tan(a) = 3/2.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, the hypotenuse is of [tex]3\sqrt{13}[/tex], while the side lengths relative to angle A are given as follows:
Opposite: 9.Adjacent: 6.Hence the trigonometric ratios are given as follows:
[tex]\sin{a} = \frac{3}{\sqrt{13}}[/tex][tex]\cos{a} = \frac{2}{\sqrt{13}}[/tex]tan(a) = 3/2.More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
CAN SOMEONE PLEASE HELP ME ASAP
(wrong answers will be reported )
The inequality is solved and the number is x ≥ 12
Given data ,
Let the number be represented as x
Now , sum of three times a number and -4 is at least twice the number plus 8
And , 3x - 4 ≥ 2x + 8
To solve for "x", we can start by isolating the "x" term on one side of the inequality
3x - 4 ≥ 2x + 8
Subtract 2x from both sides , we get
3x - 2x - 4 ≥ 2x - 2x + 8
x - 4 ≥ 8
Add 4 to both sides , we get
x - 4 + 4 ≥ 8 + 4
x ≥ 12
Hence , the inequality is x ≥ 12
To learn more about inequality equations click :
https://brainly.com/question/11897796
#SPJ1
Let f (x) = x - 4 . Graph g(x) = f (5x)
Choose the description of the transformation from the graph of f to the graph of g.
A.) The graph of g is a horizontal stretch of the graph of f by a factor of 5.
B) The graph of g is a horizontal shrink of the graph of f by a factor of 1/5
C) The graph of g is a vertical stretch of the graph of f by a factor of 5
D) The graph of g is a vertical shrink of the graph of f by a factor of 1/5
And what points would be plotted on a graph?
The graph of g(x) is on the image at the end, and the correct option for the transformation is B.
Which is the transformation applied?We define a horizontal dilation of scale factor k as:
g(x) = f(k*x)
if k > 1, we have a stretch.
if 0 < k < 1, we have a shink of scale factor 1/k
Here we have:
g(x) = f (5x) = 5x - 4
We can notice that k = 5, then we have a stretch, thus, the correct option is B.
The graph of function g(x) can be seen in the image at the end.,
LEarn more about dilations at:
https://brainly.com/question/3457976
#SPJ1
pls help i need to get this finished fast
The expression that uses the commutative property to make it easier to evaluate is (-1/3) × (-9) × 2/5.
What is commutative property?The commutative property is derived from the word "commute" which implies moving around or swapping numbers. The commutative property involves moving the numbers around while the result still remains the same.
Mathematically, if switching the arrangement of the operands does not alter the result of the arithmetic operation then that certain arithmetic operation is commutative.
From the given information, the commutative property that can be used for (-1/3) × 2/5 × (-9) to make it easier to solve is (-1/3) × (-9) × 2/5.
This is because the commutative property follows the analogy:
A × B × C = A × C × B
In addition, it will be easier to solve (-1/3) × (-9) first, then multiply it with 2/5.
Learn more about the commutative property here:
https://brainly.com/question/778086
#SPJ1
In the figure below, points X, Z, Q, R, and S lie in plane P. Points T and Y do not lie in plane P.
For each part below, fill in the blanks to write a true statement.
The blank spaces in the statements area. S, R, and Q are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.
What are Colinear Points?Points that lie on the same straight line are collinear points.
If two lines are lie on the same plane, they are referred to as coplanar lines.
(a.) S, R, and Q are on a straight line. Therefore S, R, and Q are distinct points that are collinear.
b. TX and QS are distinct lines that intersect.
c. Point Y and line QS are on the same plane. Therefore:
Point Y and line QS are coplanar.
d. Another name for plane P is: plane QSY.
Learn more about Colinear Points on https://brainly.com/question/24244967
#SPJ1
11
Select the correct answer.
The values in the table define the function fix). If g(x) is the inverse of f(x), what is the value of g(1)?
x f(x)
-1 -3
1
-1
4 1
6
4
7 6
OA 1
OB. 2
OC. 3
OD. 4
OE
5
Reset
Nerm
Answer:
D) 4
Step-by-step explanation:
Since g(x) is the inverse of f(x), g(f(x))=x. Therefore, we need to find the value of x such that f(x) = 1. Looking at the table, we can see that f(4) = 1, so g(1) = 4.
Therefore, the correct answer is (D) 4.
In ms. Morales's class the ratio of boys to girls is 3:7. The class sizes at Ms.morales's school range from 22 to 34 students per class. What is the total number of students in Ms. Morales class
The total number of students in Ms. Morales's class is either 20 or 30, depending on the value of x.
Let the ratio of boys to girls in Ms. Morales's class be 3x:7x, where 3x represents the number of boys and 7x represents the number of girls.
The total number of students in the class is equal to the sum of the number of boys and the number of girls, which is 3x + 7x = 10x.
We don't know the value of x, but we do know that the class size is between 22 and 34 students.
Therefore, we can set up an inequality based on the total number of students:
22 ≤ 10x ≤ 34
Dividing all parts of the inequality by 10, we get:
2.2 ≤ x ≤ 3.4
Since x represents a whole number of students, the possible values for x are 3 (if there are 30 students in the class) or 2 (if there are 20 students in the class).
If x = 3, then the total number of students is:
10x = 10(3) = 30
If x = 2, then the total number of students is:
10x = 10(2) = 20
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Y=(0,3) slope=4
What’s the equation
An equation of the line in slope-intercept form include the following: y = 4x + 3.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (0, 3) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 4(x - 0)
y - 3 = 4x
y = 4x + 3
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
Review the graph of circle A. On a coordinate plane, a circle has center A (1, 1) and point B (5, 4) is on the edge of the circle. A line goes from point A to point B. Which equation represents circle A? a (x – 1)2 + (y – 1)2 = 5 b (x + 1)2 + (y + 1)2 = 5 c (x – 1)2 + (y – 1)2 = 25 d (x + 1)2 + (y + 1)2 = 25
The equation represents circle A is (x + 1)² + (y + 1)² = 25. (option d)
To represent a circle on a coordinate plane, we use an equation called the equation of the circle. This equation is derived from the distance formula, which you might have learned in your geometry class. The equation of a circle with center (a, b) and radius r is given by:
(x - a)² + (y - b)² = r²
In this question, the center of the circle is given as A (1, 1). So, the equation of the circle will be of the form:
(x - 1)² + (y - 1)² = r²
To find the value of r, we can use the fact that point B (5, 4) lies on the edge of the circle. The distance between the center of the circle (1, 1) and point B (5, 4) is equal to the radius of the circle. Using the distance formula, we can find the distance between these two points:
r = √((5 - 1)² + (4 - 1)²) = √(16 + 9) = √(25) = 5
So, the equation of the circle can be written as:
(x - 1)² + (y - 1)² = 5²
Simplifying this equation, we get:
(x - 1)² + (y - 1)² = 25
Therefore, the correct answer is option d) (x + 1)² + (y + 1)² = 25.
To know more about equation here
https://brainly.com/question/10413253
#SPJ1
Answer:
C
Step-by-step explanation:
Look at the picture
what is -33 divided by (-3)
Answer: 11
Step-by-step explanation:
-3 x 11 = -33
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. H0: p= 0.8 versus H1 : p>0.8 n=125; x=105; a=0.05 calculate the test statistic, z0
The test statistic is z₀ = 2.65 and the P-value is 0.004. The null hypothesis is rejected at the 5% level of significance, and we conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8.
To test the hypothesis using the P-value approach, we can follow these
Check whether the sample size is large enough for the normal approximation to the binomial distribution. The requirements are satisfied if np₀ >= 10 and n(1-p₀) >= 10,
where p₀ is the hypothesized proportion under the null hypothesis. In this case, p₀ = 0.8, n = 125, so np₀ = 100 and n(1-p₀) = 25, both of which are greater than 10.
The null hypothesis is H₀: p = 0.8 (the true proportion is 0.8).
The alternative hypothesis is H₁: p > 0.8 (the true proportion is greater than 0.8).
Under the null hypothesis, the test statistic follows a standard normal distribution.
The test statistic is calculated as:
z₀ = (x - np₀) / sqrt(np₀(1-p₀))
where x is the number of successes in the sample.
Plugging in the values, we get:
z₀ = (105 - 1250.8) / √(1250.8 x 0.2)
z₀ = 2.65
Calculate the P-value.
The P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming the null hypothesis is true.
Since this is a right-tailed test (H₁: p > 0.8), we calculate the area to the right of the test statistic.
Using a standard normal table or calculator, we find that the area to the right of z₀= 2.65 is 0.004.
Therefore, the P-value is 0.004.
Make a decision and interpret the results.
Using a significance level of α = 0.05, we compare the P-value to α.
Since the P-value (0.004) is less than α (0.05), we reject the null hypothesis.
We conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8 at a 5% level of significance.
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ1
The rectangle has an area of 35x3 square meters
76 meters is the perimeter of the rectangle given.
The length of the rectangle is 3 meters and the width is 35 meters.
To find the perimeter, we can use the formula:
Perimeter = 2(Length + Width)
Substituting the values we obtained:
Perimeter = 2(3 + 35) = 2(38) = 76 meters
Therefore, the perimeter of the rectangle is 76 meters.
Learn more about Area here:
https://brainly.com/question/27683633
#SPJ1
Complete question:
The rectangle has an area of 35x3 square meters. Find its perimeter.
Please help me!!! quick and right answer only
Answer:
average rate of change = (16 - 1)/(4 - 1)
= 15/3 = 5
What is the outlier point? Please express your answer as (x,y).
The outlier of the graph is
(5, 1)What is outlier?An outlier is an isolated data point that significantly differs from the entirety of the points within a dataset. It is an observation that resides an exceptional distance away compared to other values in a random sample from a population.
Outliers can be identified employing various statistical techniques, like graphical methods (for instance, box plots, scatterplots) and numerical procedures (e.g., Z-score, IQR method).
The problem used a scatter plot plot to show that the outlier is (5, 1)
Learn more about outlier at
https://brainly.com/question/22324006
#SPJ1
The very top one I need help with it
As the class sizes range from 22 to 34 students, the answer must be 30,
Let the number of girls in the class "3x" and the number of boys "7x".
Then the total number of students in the class is:
Total students = 3x + 7x = 10x
We don't know the value of "x" yet, but we do know that the total number of students is between 22 and 34.
So we can set up an inequality:
22 ≤ 10x ≤ 34
Divide both sides of the inequality by 10:
2.2 ≤ x ≤ 3.4
Therefore, x can be either 3 or 4.
If x = 3, then the total number of students is:
Total students = 3x + 7x = 30
If x = 4, then the total number of students is:
Total students = 3x + 7x = 40
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. H0: p= 0.8 versus H1 : p>0.8 n=125; x=105; a=0.05 calculate the test statistic, z0
A hypothesis is a put forth explanation of a phenomenon (plural: hypotheses). Therefore, p-value given is 0.0062.
A hypothesis is a put forth explanation of a phenomenon (plural: hypotheses). A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.
H:p<=0.8
Ha: p>0.8
alpha=0.01 P{reject H:H is true}
critical value z>2.326
z=(0.9-0.8)/sqrt (0.8*0.2/100); sqrt of 0.0016=.04
z=(0.1/.04)=2.5
probability z> 2.5 is 0.0062
check with one sample proportion test on calculator, z=2.5
Reject H
p-value given is 0.0062
To know more about hypothesis, here:
https://brainly.com/question/29519577
#SPJ1
Petra is making a batch of extra large donuts by stamping circles in dough using a pastry stamp with a diameter of 5 inches. For the donut hole, she stamps out a circle using a pastry stamp that has a diameter of 2 inches.
How many square inches of dough are left in the donut after the hole has been removed?
Answer:
π(5^2 - 2^2) = 21π square inches, or about 65.97 square inches
If P = (-4, 6), find the image
of P under the following rotation.
90° counterclockwise about the
origin
([?],
Enter the number that belongs in
the green box.
The image of the given point P = (-4, 6) as required to be determined in the task content is; (-6, -4).
What is the image of the point P under the given rotation?It follows from the task content that the image point of P = (-4, 6) after a 90° counterclockwise rotation is to be determined.
Recall, for a point (x, y) , the image point after a 90° counterclockwise rotation is; (-y, x).
Ultimately, since the point P is; P = (-4, 6).
The image point is; (-6, -4).
Read more on counterclockwise rotation;
https://brainly.com/question/21850160
#SPJ1
A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
URGENT!!!! Find the y-intercept of the line that passes through the points (-3, 7) and (3, −9).
Answer:
[tex]m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} [/tex]
[tex]7 = - \frac{8}{3} ( - 3) + b[/tex]
[tex]7 = 8 + b[/tex]
[tex]b = - 1[/tex]
[tex]y = - \frac{8}{3} x - 1[/tex]
The y-intercept is -1.
While much of organized crime involves dealing with illegal goods and practices, some of it, like pirated music or videos, occurs with products
consumers access through questionable websites or at street markets. What does this information reveal about consumers?
OA
OB.
O. C.
O D.
Consumers are willing to buy illegal goods if they are cheaper.
Consumers are not aware that organized crime is a problem.
Consumers don't realize that organized criminals replace legitimate goods.
Consumers don't realize that organized criminals take over legitimate businesses.
P(A)=.60, P(B)=.30, and P(A and B)=.10. What is P9A or B)?
The probability of events A or B occurring is 0.80 or 80%.
Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
Probability can be calculated by dividing the number of favourable outcomes by the total number of possible outcomes.
To find P(A or B), we need to use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Substituting the given values, we get:
P(A or B) = 0.60 + 0.30 - 0.10
= 0.80
Therefore, the probability of events A or B occurring is 0.80 or 80%.
To know more about probability follow
https://brainly.com/question/251701
#SPJ1
The table shows some values of x and y that satisfy the equation y = acosx" + b X 10 30 Find the value of y when x = 45 80 7 90 4 120 1 150 4-3√3 180
Zoe kicks a football. Its height in feet is given by h(t) = − 16t² + 56t where
t represents the time in seconds after kick. What is the football's greatest
height?
The maximum height of the ball can reach is 49 feet high.
Which is the greatest height?We know that the height is modeled by the quadratic equation:
h(t) = -16t² + 56t
Remember that for the general quadratic equation is written as:
y = ax² + bx +c
The vertex is at the value x of:
x = -b/2a
The maximum height is at the vertex, which in this case is at the value:
t = -56/(2*-16)
t = 1.75
Evaluating the height equation in that time, we get:
h = -16*(1.75)² + 56*1.75
h = 49
The maximum height that the ball can reach is 49ft
Learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ1
11. At Sunnyside Middle School, 16 cheerleaders 1 need to raise a total of $9,500 for a trip. So far, they have raised $8,340. How much money, in dollars, per cheerleader, still needs to be raised for the trip?
Answer:
To find out how much money per cheerleader still needs to be raised for the trip, we need to divide the remaining amount by the number of cheerleaders:
Total amount needed = $9,500
Amount raised so far = $8,340
Amount still needed = $9,500 - $8,340 = $1,160
Number of cheerleaders = 16
Amount per cheerleader still needed = $1,160 ÷ 16 = $72.50
Therefore, $72.50 per cheerleader still needs to be raised for the trip.
x P(x)
0 0.3
1 0.25
2 0.2
3 0.25
Find the standard deviation of this probability distribution.
Daniella receives $30. Show that Edward recieves $45
The proof that Daniel and Edward receive money in the ratio of their ages is shown below.
What is a Ratio?A ratio expresses the number of times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, while the orange-to-total fruit ratio is 8:14.
Given that Daniel and Edward receive money in the ratio of their ages. And the age of Daniel and Edward is 8 years and 12 years, respectively. Therefore, it can be written as,
Ratio of Ages
=Age of Daniel: Age of Edward
= 8 years : 12 years =
= 2 : 3
Ratio of the amount received by them
= Amount received by Daniel: Amount received by Edward
= $30 : $45
= 2 : 3
Since, Ratio of Ages = Ratio of the amount received by them.
Therefore, it can be concluded that Daniel and Edward receive money in the ratio of their ages.
Learn more about Ratios:
https://brainly.com/question/1504221
#SPJ1
The complete question is:
Daniel is 8 years old and Edward is 12 years old. Their parents give them money in the ratio of their ages. If Daniella receives $30, then Show that Edward receives $45.