At the ice cream shoppe ,one banana split and five milkshakes cost $16.24.If three banana splits and two milkshakes cost $15.05,find the cost of a milkshake.

Answer:

Part 1) [tex]A=28.96^o[/tex]

Part 2) [tex]B=46.57^o[/tex]

Part 3) [tex]C=104.47^o[/tex]

Step-by-step explanation:

step 1

Find the measure of angle A

Applying the law of cosines

[tex]a^2=b^2+c^2-2(b)(c)cos(A)[/tex]

we have

[tex]a=10\ cm\\b=15\ cm\\c=20\ cm[/tex]

substitute

[tex]10^2=15^2+20^2-2(15)(20)cos(A)[/tex]

Solve for A

[tex]2(15)(20)cos(A)=15^2+20^2-10^2[/tex]

[tex]600cos(A)=525[/tex]

[tex]cos(A)=(525/600)[/tex]

using a calculator

[tex]A=cos^{-1}(525/600)=28.96^o[/tex]

step 2

Find the measure of angle B

Applying the law of cosines

[tex]b^2=a^2+c^2-2(a)(c)cos(B)[/tex]

we have

[tex]a=10\ cm\\b=15\ cm\\c=20\ cm[/tex]

substitute

[tex]15^2=10^2+20^2-2(10)(20)cos(B)[/tex]

Solve for A

[tex]2(10)(20)cos(B)=10^2+20^2-15^2[/tex]

[tex]400cos(B)=275[/tex]

[tex]cos(B)=(275/400)[/tex]

using a calculator

[tex]B=cos^{-1}(275/400)=46.57^o[/tex]

step 3

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]A+B+C=180^o[/tex]

we have

[tex]A=28.96^o[/tex]

[tex]B=46.57^o[/tex]

substitute

[tex]28.96^o+46.57^o+C=180^o[/tex]

[tex]C=180^o-75.53^o[/tex]

[tex]C=104.47^o[/tex]

Answer:

A

Step-by-step explanation:

i took the test. make me branliest please

Answer:

49 ft; B: 30.5 ft

Step-by-step explanation:

Find nth terms and arithmetic means of arithmetic sequences and find sums of n terms of arithmetic series.

Answer:

Part 1) [tex]BC=12.2\ units[/tex]

Part 2) [tex]m\angle A=55^o[/tex]

Part 3) [tex]m\angle C=35^o[/tex]

Step-by-step explanation:

Part 1) Find AC

we know that

In the right triangle ABC of the figure

Applying the Pythagorean Theorem

[tex]AC^2=AB^2+BC^2[/tex]

substitute the given values

[tex]AC^2=7^2+10^2[/tex]

[tex]AC^2=149\\AC=12.2\ units[/tex]

Part 2) Find the measure of angle A

we know that

In the right triangle ABC

[tex]tan(A)=\frac{BC}{AB}[/tex] ----> by TOA (opposite side divided by the adjacent side)

substitute the values

[tex]tan(A)=\frac{10}{7}[/tex]

using a calculator

[tex]m\angle A=tan^{-1}(\frac{10}{7})=55^o[/tex]

Part 3) Find the measure of angle C

we know that

In the right triangle ABC

[tex]m\angle A+m\angle C=90^o[/tex] ----> by complementary angles

substitute the given value

[tex]55^o+m\angle C=90^o[/tex]

[tex]m\angle C=90^o-55^o=35^o[/tex]

Option b: The solution to the system of equations is (2,0)

Explanation:

Given that the graph that contains the system of equations.

We need to determine the solution to the system of equations.

The solution to the system of equations is the points of intersection of these two lines.

The two lines intersect at x - axis at 2 and y - axis 0.

This can be written in coordinates as (2,0)

Thus, the point of intersection of the two lines is the point (2,0)

Hence, Option b is the correct answer.

Answer: 27.3 degrees

cos x = 16/18

x = arccos(16/18)

x = 27.3 degrees

Value of x is 30°

Step-by-step explanation:

cos x° = adjacent side/hypotenuse = 16/18 = 8/9

x° = cos inverse(8/9) = 27.12° = 30° (Rounded off to nearest ten)

Answer:

5.0 ft - 5.6 ft

Step-by-step explanation:

Given that the structure is to be made using two 12 foot boards, then we expect the total perimeter to be equal to (2*12)= 24 ft.

Using the angle of elevation, 40° and the width of 8 ft then you can apply the formula for tangent of a triangle where ;

Tan α = opposite side length/adjacent length

Tan 40°= h/8

h= 8 tan 40° = 6.71 ft

Applying the cosine of an angle formula to find the length of the sliding side

Cosine β = adjacent length /hypotenuse

Cosine 40°= 8/ sliding side length

sliding side length = 8/cosine 40° =10.44 ft

Checking  the perimeter = 10.44 +8+6.71= 25.15 ft

This is more than the total lengths of the boards, so you need to adjust the height as;

24 - 18.44 = 5.56 ft ,thus the height should be less or equal to 5.56 ft

h≤ 5.6 ft

The height range for Alex's outdoor structure that ensures snow slides off with a minimum width of 8 feet is approximately 3.4 to 12 feet, calculated using the tangent function in trigonometry for the minimum height and considering the maximum height based on the board length.

To solve this, we employ trigonometry, specifically the tangent function because it relates the angle of elevation to the opposite side (height in this case) over the adjacent side (half the width here, since it's a symmetrical layout).

First, establish the minimum height using the minimum angle of elevation, 40 degrees:
tan(40 degrees) = h / (8/2)

Solving for h gives h = tan(40 degrees) × 4. Calculating this yields approximately 3.4 feet, which is the minimum height.

Next, considering the boards are 12 feet long, to find the maximum height, we can imagine them being placed vertically, thus:
h = 12 feet as the absolute maximum height since any angle of elevation would still allow snow to slide off.

Therefore, the range of heights for the structure is approximately 3.4 to 12 feet.

The possible length of the third side of a triangle with sides of 9 units and 6 units must be more than 3 units and less than 15 units, according to the triangle inequality theorem.

To determine the possible length of the third side of a triangle when two sides are known, we can use the triangle inequality theorem. The theorem states that the length of any side of a triangle must be less than the sum of the other two sides and greater than their difference. In this case, Millie's triangle has sides of 9 units and 6 units.

The sum of these two sides is 9 units + 6 units = 15 units, and their difference is 9 units - 6 units = 3 units. Therefore, the third side of the triangle must be greater than 3 units but less than 15 units.

The third side must be greater than 3 units.

The third side must be less than 15 units.

To summarize, the third side could have any length that is more than 3 units but less than 15 units.

Answer:

2 seconds.

Step-by-step explanation:

Given [tex]d=4t+16t^{2}[/tex] and d = 72 ft

We need to solve [tex]72=4t+16t^{2}[/tex]

[tex]4t+16t^{2}-72=0[/tex]

[tex]4t^{2}+t-18=0[/tex]

[tex]4t^{2}+9t-8t-18=0[/tex]

[tex]t(4t+9)-2(4t+9)=0[/tex]

[tex](t-2)(4t+9)=0[/tex]

[tex]t-2=0,4t+9=0[/tex]

[tex]t=2,t=-\frac{9}{4}[/tex]

Since, time can not be negative, so the required time is t = 2 seconds.

Final answer:

To find the time it takes for the object to travel 72 feet based on the given distance formula d=4t+16t², you can solve for t by substituting the distance value of 72 feet into the formula and solving for t.

Explanation:

Distance: To find the time it takes for the object to travel 72 feet, we can set the distance formula d = 4t + 16t² equal to 72 feet and solve for t.

Step-by-step explanation:

Given: d = 4t + 16t² and d = 72 feet

Substitute d = 72 into the formula: 72 = 4t + 16t²

Rearrange the equation: 16t² + 4t - 72 = 0

Solve for t using the quadratic formula or factoring.

The solutions for t will give you the time it takes for the object to travel 72 feet.

Answer:

a) [tex]\hat \mu = \bar X = 145[/tex]

b) [tex]145-1.64\frac{35}{\sqrt{25}}=133.52[/tex]  

[tex]145+1.64\frac{35}{\sqrt{25}}=156.48[/tex]  

So on this case the 90% confidence interval would be given by (133.52;156.48)  

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]\bar X=145[/tex] represent the sample mean  

[tex]\mu[/tex] population mean (variable of interest)  

[tex]\sigma=35[/tex] represent the population standard deviation  

n=25 represent the sample size  

a) For this case the best point of estimate for the population mean is the sample mean:

[tex]\hat \mu = \bar X = 145[/tex]

b) Calculate the confidence interval

The confidence interval for the mean is given by the following formula:  

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)  

Since the confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that [tex]z_{\alpha/2}=1.64[/tex]

Now we have everything in order to replace into formula (1):  

[tex]145-1.64\frac{35}{\sqrt{25}}=133.52[/tex]  

[tex]145+1.64\frac{35}{\sqrt{25}}=156.48[/tex]  

So on this case the 90% confidence interval would be given by (133.52;156.48)  

Answer:

[tex]t=\frac{2.64-2.5}{\frac{1.02}{\sqrt{15}}}=0.532[/tex]    

[tex]p_v =P(t_{(14)}>0.532)=0.302[/tex]  

If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis at 5% of significance

Step-by-step explanation:

Data given and notation  

[tex]\bar X=2.64[/tex] represent the sample mean

[tex]s=1.02[/tex] represent the sample standard deviation for the sample  

[tex]n=15[/tex] sample size  

[tex]\mu_o =2.5[/tex] represent the value that we want to test

[tex]\alpha[/tex] 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 check if the mean is greater than 2.5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 2.5[/tex]  

Alternative hypothesis:[tex]\mu > 2.5[/tex]  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (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:  

[tex]t=\frac{2.64-2.5}{\frac{1.02}{\sqrt{15}}}=0.532[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=15-1=14[/tex]  

Since is a one side right tailed test the p value would be:  

[tex]p_v =P(t_{(14)}>0.532)=0.302[/tex]  

Conclusion  

If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis at 5% of significance

Answer: $17505 must be deposited today.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited.

From the information given,

A = 30000

r = 8% = 8/100 = 0.08

n = 1 because it was compounded once in a year.

t = year

Therefore,.

30000 = P(1 + 0.08/1)^1 × 7

30000 = P(1.08)^7

30000 = 1.7138P

P = 30000/1.7138

P = $17505

Final answer:

To have $30,000 in 7 years for a down payment on a house, approximately $19,882.68 must be deposited today into an account with annual compounding and an APR of 8%.

Explanation:

To calculate the amount that must be deposited today, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money desired, P is the principal amount (the amount to be deposited), r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years. In this case, A = $30,000, r = 0.08 (8% as a decimal), n = 1 (compounded annually), and t = 7 years:

A = P(1 + r/n)^(nt) ⇒ $30,000 = P(1 + 0.08/1)^(1*7)

Now, we can solve the equation for P:

P = $30,000 / (1 + 0.08/1)^(1*7) ≈ $19,882.68

Therefore, approximately $19,882.68 must be deposited today to have $30,000 in 7 years for the down payment on a house.

For this case we have that by definition, the volume of a cube is given by:

[tex]V = l ^ 3[/tex]

Where:

l: It's the side of the cube

According to the statement we have:

[tex]l = 18 \ m[/tex]

Substituting we have:

[tex]V = 18 ^ 3\\V = 5832 \ m ^ 3[/tex]

Thus, the volume of the cube is [tex]5832 \ m ^ 3[/tex]

ANswer:

The volume of the cube is [tex]5832 \ m ^ 3[/tex]

Complete Question:

The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.

Answer:

The total number of vehicles sold = 32

Step-by-step explanation:

Since the ratio of sales is 4:5:7

Let m be a common factor

The number of sedans sold = 4m

The number of trucks sold = 5m

The number of vans sold = 7m

In (1)

Since the number of vans sold was between 10 and 20. i.e 10 ≤ 7m ≤20

The only multiple of 7 between 10 and 20 is 14

Therefore, 7m = 14; m=2

in (2)

The number of sedans sold was less than 10 i.e. 0 < 4m < 10

There are two multiples of 4 between 0 and 10, they are 4 and 8

for 4m = 4; m=1

for 4m = 8; m=2

m = 2 is the only consistent value in (1) and (2)

The number of sedans sold = 4m = 4 *2 = 8

The number of trucks sold = 5m = 5 * 2 = 10

The number of vans sold = 7m = 7*2 = 14

The total number of vehicles sold = 8 + 10 + 14

The total number of vehicles sold = 32

COMPLETE QUESTION

The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.

Answer:

32 Vehicles

Step-by-step explanation:

Take a look at the image to see the explanation

Answer:

B

Step-by-step explanation: pORBABLITY

Using the Central Limit Theorem, it is found that:

a) 174.

b) 26.

c) Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the central limit theorem is applied, and the sampling distribution can be approximated by a normal distribution.

d) 0.87

e) 0.0238

f) 0.2005 = 20.05% probability that the proportion of people in the sample with a high school diploma is less than 85%.

-------------------------------------

The Central Limit Theorem establishes that for a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex] , if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]

In this problem:

Item a:

This is

[tex]np = 200(0.87) = 174[/tex]

Item b:

This is:

[tex]n(1-p) = 200(0.13) = 26[/tex]

Item c:

Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the central limit theorem is applied, and the sampling distribution can be approximated by a normal distribution.

Item d:

The mean is:

[tex]\mu = p = 0.87[/tex]

Item e:

The standard deviation is:

[tex]s = \sqrt{\frac{0.87(0.13)}{200}} = 0.0238[/tex]

Item f:

Using z-scores, the probability is the p-value of Z when X = 0.85.

We have that:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.85 - 0.87}{0.0238}[/tex]

[tex]Z = -0.84[/tex]

[tex]Z = -0.84[/tex] has a p-value of 0.2005.

0.2005 = 20.05% probability that the proportion of people in the sample with a high school diploma is less than 85%.

A similar problem is given at https://brainly.com/question/15581844

Question:

A certain vibrating system satisfies the equation u''+γu'+u=0. Find the value of the damping coefficientγfor which the quasi period of the damped motion is 50% greater than the period of the corresponding undamped motion.

Answer: y = √(20/9) = √20/3 = 1.49071

Step-by-step explanation:

u''+γu'+u=0

m =1, k =1, w• = √ (k/m) = 1

The period of undamped motion T, is given by T = 2π/w•, T = 2π/1 = 2π

The quasi period Tq = 2π/quasi frequency

Quasi frequency = ((4km - y^2)^1/2)/2m

Therefore the quasi period Tq = 4πm/((4km - y^2)^1/2)

From the question the quasi period is 50% greater than the period of undamped motion

Therefore Tq = T + (1/2)T = (3/2)T

Thus,

4πm/((4km - y^2)^1/2) = (3/2)(2π)

Where, k =1, m=1,

4π/((4 - y^2)^1/2) = 3π,

(4 - y^2)^1/2 = 4π/3π,

(4 - y^2) = (4/3)^2,

4 - y^2 = 16/9,

y^2 =4 - 16/9,

y^2 = 20/9,

y = √(20/9)

Answer:

Answer is 1.49071

Step-by-step explanation:

See the picture for the complete details

Answer:

2 workers

Step-by-step explanation:

Here is additional information for your question:

The questions below deal with the Gizmo Company, which has the following production function.

# Workers # Produce

0 0

1 10

2 19

3 26

4 31

5 34

If the real wage is equal to 8 widgets and only an integer number of workers can be hired the Gizmo company should hire?

My answer:

2 workers. (where MPL is less than real wage)

The calculated area of the semicircle is 584.20 square inches

How to determine the area

From the question, we have the following parameters that can be used in our computation:

Length A to D to B = 37 inches

Perimeter of the semicircle = 60.57 inches

The perimeter of the semicircle is calculated using

P = πr

So, we have

πr = 60.57

r = 60.57/π

r = 60.57/3.14

r = 19.29

The area is then calculated as

Area = πr²/2

This gives

Area = π * 19.29²/2

Using 3.14 for π, we have

Area = 3.14 * 19.29²/2

Evaluate

Area = 584.20

Hence, the area of the semicircle is 584.20 square inches

Answer:

sampling error i think

Step-by-step explanation:

It would be C. isosceles triangle.

Answer: the speed of the current is 6 mph

Step-by-step explanation:

Let x represent the speed of the current.

Logan is driving a boat that has a speed of 18 mph in standing water.

Assuming the current slowed down the boat while she was going up(upstream), it means that his total speed was (18 - x) mph

Also, if the current helped the boat while she was going down(downstream), it means that his total speed was (18 + x) mph

Time = distance/speed

The boat travels 4 miles each way. The time taken to travel upstream is

4/(18 - x)

Time taken to travel downstream is

4/(18 + x)

The round trip took 0.5 hour. It means that

4/(18 - x) + 4/(18 + x) = 0.5

Multiplying through by (18 - x)(18 + x), it becomes

4/(18 - x) + 4/(18 + x) = 0.5(18 - x)(18 + x)

4(18 + x) + 4(18 - x) = 0.5(18 - x)(18 + x)

72 + 4x + 72 - 4x = 0.5(324 + 18x -

18x - x²)

144 = 0.5(324 - x²)

144 = 162 - 0.5x²

0.5x² = 162 - 144

0.5x² = 18

x² = 18/0.5 = 36

x = √36

x = 6

Answer:

[tex]\frac{9}{4}[/tex]

Step-by-step explanation:

Given

x² + 3x - 13 = 0 ( add 13 to both sides )

x² + 3x = 13

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2([tex]\frac{3}{2}[/tex] )x + ([tex]\frac{3}{2}[/tex] )² = 13 + ([tex]\frac{3}{2}[/tex] )², that is

x² + 2([tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] = 13 + [tex]\frac{9}{4}[/tex]

(x + [tex]\frac{3}{2}[/tex] )² = [tex]\frac{61}{4}[/tex]

The required number to be added to complete the square is [tex]\frac{9}{4}[/tex]

Hence, required number to be added to complete the square is 9/4

A quadratic equation is any equation that can be rewritten in standard form as ax2+bx+c=0 in algebra. When x is an unknown and a, b, and c are known numbers, and an is less than 0. Because there is no ax2 term when a = 0, the equation is linear rather than quadratic.

Given equation =x² + 3x - 13 = 0 ( add 13 to both sides )

=x² + 3x = 13

using complete the square and add ( half the coefficient of the x- term )² to both sides

=x² + 2(3/2 )x + ( 3/2)² = 13 + (3/2 )², that is

=x² + 2(3/2 )x +  = 13 + 9/4

=(x + 3/2 )² = 61/4

The required number to be added to complete the square is 9/4

learn more about quadratic equation

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Answer:

Harris ate [tex]\dfrac{n-4}{4}[/tex] slices of pizza.

Step-by-step explanation:

If 4 friends evenly divided up an n-slice pizza

Total Slices=n

Number of people sharing=4

Each Friend will receive [tex]\dfrac{n}{4}[/tex] slice of pizza

Harris Ate 1 fewer slice than he received

Harris' Share= [tex]\dfrac{n}{4}[/tex]

Number of Slices Harris Ate ate[tex]\dfrac{n}{4}-1\\=\dfrac{n-4}{4}[/tex]

Answer:

N-4

___

4

Step-by-step explanation:

Answer:

decreases as the required rate of return increases.

Step-by-step explanation:

Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. This differences tend to reduce as the requires rate of return increases.

Answer:

13 Minutes

Step-by-step explanation:

If it took 28 minutes total to wait in line and be in the haunted house, then the equation would be 15+x=28

x=13

Answer:

13 Minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

We will find two equations for this system, one representing flour and the other representing cocoa.  For the flour, we start with $2.50, and the cost goes up .07 per month, x. The equation for that is

y = .07x + 2.50

For the cocoa, the equation is written in the exact same way, but the cost goes down.  Down is a negative thing while up is a positive thing.  The cost starts at $6.00 and goes down .03 per month, x. The equation for that is

y = -.03x + 6.00

Comparing the first equation to the second, the .07 is positive because the cost goes UP that amount per month and the .03 is negative because the cost goes DOWN that amount per month.  Get it?

If y is cost and we are tryong to find out where the cost is the same, we are looking for when y is the same.  If the first y is equal to .07x + 2.50 and the second y is equal to -.03x + 6.00, and y is equal to y, then

.07x + 2.50 = -.03x + 6.00 (this is setting the first y equal to the second y).  This is the system that describes how to find the number of months x when the cost y is the same. We'll solve it just for practice.

Combining like terms we get

.10x = 3.5 so

x = 35

Now back sub in what x equals to solve for y.  If x = 35, then in the first equation,

.07(35) + 2.50 = y and

y = 4.95 (you could have used the second equation and subbed in 35 for x and you will get the exact same y value.  Promise!)

What this answer tells us is that 35 months after the start of this pricing, the cost of flour will be the same as the cost of cocoa.  But immediately after 35 months, the costs will not be the same anymore.  It is only AT 35 months.  At 36 months, the costs will be different.

The requried system of equations used to find the number of months is
y = 2.50 + 0.07x  and y = 6 -0.03x.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Let the number of months, x, when the price, y.
The cost of flour is $2.50 per pound and increases at a rate of $0.07 per month.
Equation ⇒ y = 2.50 + 0.07x   - - - - - (1)

The cost of cocoa is $6.00 per pound and decreases at a rate of $0.03 per month.
Equation ⇒ y = 6 -0.03x  - - - - - (2)

Solution of the equation 1 and 2 gives the price which would be equal for both flour and cocoa.

Thus, the requried system of equations used to find the number of months is y = 2.50 + 0.07x  and y = 6 -0.03x.

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Answer:

Part 1) [tex]m\angle 1=39^o[/tex]

Part 2) [tex]m\angle 3=51^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

Part 1) Find the measure of angle 1

we know that

The longer diagonal of a kite bisects the kite into two equal parts

That means

[tex]m\angle 1=39^o[/tex]

In this problem the longer diagonal is the segment AC

Part 2) Find the measure of angle 3

we know that

The intersection of the diagonals of a kite form 90 degrees.

That means ----> The triangle ADO (O is the intersection point both diagonals) is a right triangle

so

[tex]39^o+m\angle 3=90^o[/tex] ----> by complementary angles in a right triangle

[tex]m\angle 3=90^o-39^o=51^o[/tex]

Answer:

Nate is in Group 2.

Step-by-step explanation:

Total number of students is 24.

These 24 students are divided equally among 4 groups.

Compute the number of students in each group:

Number of students in each group [tex]=\frac{24}{4}=6[/tex]

Thus, there will be 6 groups.

Now the students are numbered with the first student in the first group numbered as 1.

The groups will be:

Group 1: 1, 2, 3, 4, 5, 6

Group 2: 7, 8, 9, 10, 11, 12

Group 3: 13, 14, 15, 16, 17, 18

Group 4: 19, 20, 21, 22, 23, 24

It is provided that Nate is the 11th student.

Then Nate is in group 2.

The value of a is 12

Step-by-step explanation:

Here we have , Lake mead contains approximately 28,945,000 acre feet of water and there are about 326,099 gallons in 1 acre foot . We need to find that the approximate number of gallons of water in lake mead is [tex]9.4 \times 10^a[/tex] what is the value of a . Let's find out :

We have, 1 acre foot = 326,099 gallons

So , 28,945,000 acre feet =  326,099 gallons ( 28,945,00 )

⇒ [tex]326,099 (28,945,000 )[/tex]

⇒ [tex]9.4389356e+12[/tex]

⇒ [tex]9.4(10^{12})[/tex]

Therefore , comparing this [tex]9.4(10^{12})[/tex] with [tex]9.4 \times 10^a[/tex]  we see that value of a = 12 .So , Value of a is 12 in  number of gallons of water in lake mead [tex]9.4 \times 10^a[/tex].

Final answer:

The number of gallons of water in Lake Mead, calculated by its volume in acre-feet times the gallons per acre-foot, is approximately 9.4 × 10¹², making the value of 'a' in the scientific notation 12.

Explanation:

To find the approximate number of gallons of water in Lake Mead, we multiply the volume of the lake in acre-feet by the number of gallons in an acre-foot. Given that Lake Mead contains approximately 28,945,000 acre-feet of water and there are about 326,099 gallons in 1 acre-foot, the calculation is as follows:

28,945,000 acre-feet × 326,099 gallons/acre-foot = 9.430455145 × 10¹² gallons.

Therefore, the scientific notation for the total number of gallons of water in Lake Mead would be approximately 9.4 × 10¹², making the value of a in the scientific notation 12.

Each of the four responses to the question about the graph's title has a different perspective. Some are based on the data presented on the graph, such as the proportions of votes or the relative sizes of the bars representing each candidate. One comment about media bias doesn't directly pertain to the information on the graph.

Without the precise context of the graph or its title, it is a bit tricky to answer this question directly. However, based on the details presented, let's analyze each statement:

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Among the sets given, ∅ is not a power set while {∅,{a}}, {∅,{a},{∅,a}}, and {∅,{a},{b},{a,b}} can be considered power sets of the sets {a}, {a}, and {a,b} respectively according to the definition of power set.

In mathematics, a power set of any set S is the set of all subsets of S, including the empty set and S itself. We can use this definition to examine the four sets provided and determine if they qualify as power sets.

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