What is the solution to the system of equations below?
x + 3y = 1
-3x - 3y = -15

Answer:

48.30

Step-by-step explanation:

First determine the tip

42 *15%

42 *.15 =6.30

Add this to the amount of the tip

42 + 6.30 =48.30

The total amount is 48.30

Answer:

Step-by-step explanation:

$48.30

Answer:

Step-by-step explanation:

Hello!

X₁: speed of a motorcycle at a certain intersection.

n₁= 135

X[bar]₁= 33.99 km/h

S₁= 4.02 km/h

X₂: speed of a car at a certain intersection.

n₂= 42 cars

X[bar]₂= 26.56 km/h

S₂= 2.45 km/h

Assuming

X₁~N(μ₁; σ₁²)

X₂~N(μ₂; σ₂²)

and σ₁² = σ₂²

A 90% confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.

The parameter of interest is μ₁-μ₂

(X[bar]₁-X[bar]₂)±[tex]t_{n_1+n_2-2}[/tex] * [tex]Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }[/tex]

[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{175; 0.95}= 1.654[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{134*16.1604+41*6.0025}{135+42-2} } = 3.71[/tex]

[(33.99-26.56) ± 1.654 *([tex]3.71*\sqrt{\frac{1}{135} +\frac{1}{42} }[/tex])]

[6.345; 8.514]= [6.35; 8.51]km/h

Construct the 98% confidence interval for the difference μ₁-μ₂ when X[bar]₁= 475.12, S₁= 43.48, X[bar]₂= 321.34, S₂= 21.60, n₁= 12, n₂= 15

[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{25; 0.99}= 2.485[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{11*(43.48)^2+14*(21.60)^2}{12+15-2} } = 33.06[/tex]

[(475.12-321.34) ± 2.485 *([tex]33.06*\sqrt{\frac{1}{12} +\frac{1}{15} }[/tex])]

[121.96; 185.60]

I hope this helps!

Answer:

[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value would be:

[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.

Step-by-step explanation:

Information given

22, 17, 27, 20, 23, 19, 24, 18, 19, and 24

The sample mean and deviation for these data are:

[tex]\bar X=21.3[/tex] represent the ample mean

[tex]s=3.199[/tex] represent the sample standard deviation for the sample  

[tex]n=10[/tex] sample size  

[tex]\mu_o =20[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if the true mean is equal to 20 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 20[/tex]  

Alternative hypothesis:[tex]\mu \neq 20[/tex]  

The statistic would be:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing the info given we got:

[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value would be:

[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.

Answer:

1) a^4 + 16b^4

2) x^4 + 5x^2 + 9

3) p^2 − 10px − q^2 + 6qx + 16x^2

Step-by-step explanation:

1) a^4 + (2b)^4

= a^4 + 16b^4

2) x^4 + 5x^2 + 9

There are no like terms.

Answer:

= x^4 + 5x^2 + 9

3) p2 − 10xp + 16x2 − q2 + 6xq

= p^2 − 10px − q^2 + 6qx + 16x^2

Answer:

79.2° (First Option)

Step-by-step explanation:

To find mAB, recognize that the percents given for the pie chart can represent the percent area of the sector of the circle, the percent measure of the central angle that forms the sector, or the percent measure of the length of the arc.

The measure of an arc is equal to the measure of the central angle between the radii that form its endpoints. So, mAB=m∠AOB.

The measure of the central angle AOB that forms AB is 22 percent of the whole circle, or (0.22)360∘. So, mAB=0.22(360∘)=79.2∘

Therefore, the measure of arc AB

is 79.2∘.

The measure of the arc AB of a circle showing the different vitamins present in a health drink is 79.2 degrees.

The measure of an arc is always equivalent to the measure of the central angle between the radii that form its endpoints.

As the measure of an arc is always equivalent to the measure of the central angle between the radii that form its endpoints.

Thus [tex]m\angle{AOB}=\widehat{AB}[/tex].

First, find the measure of angle AOB.

Since the measure of angle AOB shows 22% of vitamins of the whole circle.

This means that the measure of angle AOB is 22% of 360 degrees.

Then we will get

[tex]m\angle{AOB}=\dfrac{22}{100}\times 360^{\circ}\\m\angle{AOB}=79.2^{\circ}[/tex]

Here the measure of angle AOB  is 79.2 degrees.

And since [tex]m\angle{AOB}=\widehat{AB}[/tex].

Therefore the measure of arc AB is 79.2 degrees.

That means option A [tex]79.2^{\circ}[/tex] is correct option.

Learn more about the measure of arc here- https://brainly.com/question/12555201

#SPJ2

36 - k = 4 + k

36 - 4 = k + k

32 = 2k

32/2 = k

16 = k

Steps:

Step 1: Simplify both sides of the equation

36−k=4+k

36+−k=4+k

−k+36=k+4

Step 2: Subtract k from both sides

−k+36−k=k+4−k

−2k+36=4

Step 3: Subtract 36 from both sides

−2k+36−36=4−36

−2k=−32

Step 4: Divide both sides by -2

−2k/−2 = −32/−2

Description:

Since we are trying to find the value of K, we need to simplify both sides of the equation. After that your answer will come as −k+36=k+4.  Now the second step is to  subtract k from both sides, your equation will come as −2k+36=4.  Thirdly we need to subtract 36 from both sides, your equation will come as −2k=−32.  Now you need to divide both sides by -2. After you do that, you will get your answer which is k=16.

Answer: k=16

Please mark brainliest

Hope this helps.

Answer:

(x+7)^2+(y-8)^2=1

(x-x value of center)^2+(y-y value of center)^2=radius

Answer:

(x + 7)² + (y - 8)² = 1

Step-by-step explanation:

(x - h)² + (y - k)² = r²

h = - 7, k = 8, r = 1

(x -(-7))² + (y - 8)² = 1²

(x + 7)² + (y - 8)² = 1

Answer:

36.87

Step-by-step explanation:

The cosine of an angle in a right triangle is the length of the adjacent side divided by the length of the hypotenuse, which in this case is 4/5. Therefore, the measure of this angle is the arc cosine of 4/5, or about 36.87 degrees. Hope this helps!

Answer:

x =20

Step-by-step explanation:

7x- 99 = 2x+1 (  vertically opposite angles)

7x - 2x = 1 +99

5x = 100

x =100/5

x =20

hope it helps

Answer:

no.

Step-by-step explanation:

Answer: -2x-18

Step-by-step explanation:

Question:

A solar power company is trying to correlate the total possible hours of daylight (simply the time from sunrise to sunset) on a given day to the production from solar panels on a residential unit. They created a scatter plot for one such unit over the span of five months. The scatter plot is shown below. The equation line of best fit for this bivariate data set was: y = 2.26x + 20.01

How many kilowatt hours would the model predict on a day that has 14 hours of possible daylight?

Answer:

51.65 kilowatt hours

Step-by-step explanation:

We are given the equation line of best fit for this data as:

y = 2.26x + 20.01

On a day that has 14 hours of possible daylight, the model prediction will be calculated as follow:

Let x = 14 in the equation.

Therefore,

y = 2.26x + 20.01

y = 2.26(14) + 20.01

y = 31.64 + 20.01

y = 51.65

On a day that has 14 hours of daylight, the model would predict 51.65 kilowatt hours

Answer:

all even numbers

Step-by-step explanation:

Answer:

Any and all of the Even numbers are scale factors of two!

Answer:

The answer will be 1.25

Step-by-step explanation:

In order to make 512 into a decimal, you take the top number or numerator, which is 5 , and take your bottom number or your denominator, which is 12 , and divide 5 by 12 which will give you0.416666667

Hey there! :)

Answer:

1.25

Step-by-step explanation:

Begin by multiplying the fractions:

[tex]\frac{3}{1}* \frac{5}{12}= \frac{3*5}{1*12} = \frac{15}{12}= \frac{5}{4}[/tex]

Convert [tex]\frac{5}{4}[/tex] into a decimal:

5/4 = 1.25.

Answer:

40+5x=y

60+3x=y

Step-by-step explanation:

The first park is 40+5x

The second park is 60+3x

Now set them both equal to y

Answer:

a) For this case and using the empirical rule we can find the limits in order to have 9% of the values:

[tex] \mu -2\sigma = 55 -2*6 =43[/tex]

[tex] \mu +2\sigma = 55 +2*6 =67[/tex]

95% of the widget weights lie between 43 and 67

b) For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:

[tex] 100 -0.15-2.5 = 97.85[/tex]

c) We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%

Step-by-step explanation:

For this case our random variable of interest for the weights is bell shaped and we know the following parameters.

[tex]\mu = 55, \sigma =6[/tex]

We can see the illustration of the curve in the figure attached. We need to remember that from the empirical rule we have 68% of the values within one deviation from the mean, 95% of the data within 2 deviations and 99.7% of the values within 3 deviations from the mean.

Part a

For this case and using the empirical rule we can find the limits in order to have 9% of the values:

[tex] \mu -2\sigma = 55 -2*6 =43[/tex]

[tex] \mu +2\sigma = 55 +2*6 =67[/tex]

95% of the widget weights lie between 43 and 67

Part b

For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:

[tex] 100 -0.15-2.5 = 97.85[/tex]

Part c

We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%

Answer:

[tex]r=\frac{-a+p}{a+p}[/tex]

Step-by-step explanation:

[tex]-pr+p=ar+a[/tex]

[tex]-ar-pr+p=a[/tex]

[tex]-ar-pr=a-p[/tex]

[tex]r(-a-p)=a-p[/tex]

[tex]r=\frac{-a+p}{a+p}[/tex]

Answer:

[tex]r = \frac{p - a}{(p + a)} [/tex]

Step-by-step explanation:

[tex]p = \frac{a(1 + r)}{(1 - r)} \\ p(1 - r) = a(1 + r) \\ p - pr = a + ar \\ p - a = pr + ar \\ p - a = r(p + a) \\ \frac{p - a}{(p + a)} = \frac{r(p + a)}{(p + a)} \\ \frac{p - a}{(p + a)} = r[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

14.25°

Step-by-step explanation:

distance from middle of the net = 8 m

width of the net = 2 m

this is a case of a triangle with height 8 m, and base 2 m. We are required to find the angle facing the base.

We can get this angle by splitting the triangle into two right angle triangles with base of 1 m, and then solve for the angle facing the base.

We use the trigonometric function;   tan∅ = opp/adj

opp is the side facing the angle = 1 m

adj is the height of the triangle (usually, it is the side besides the opposite side and the longest side; the hypothenus)

adj = 8 m

tan∅ = [tex]\frac{1}{8}[/tex] = 0.125

∅ = [tex]tan^{-1}[/tex] 0.125 = 7.125°

Angle within which Lars must fire his shot = 2 x ∅

= 2 x 7.125° = 14.25°

Answer:

displacement x = - 0.046sin4t +0.006cos4t

Step-by-step explanation:

The model of the equation of motion is a forced motion equation and to determine the displacement of the weight as a function of time; we have:

the weight balances of the  elastic force in the spring  to be expressed by the relation:

mg = kx

where;

x=4 in (i.e  1/3 ft )

mass m = 6lb

let make k the subject; then:

k = mg/x = 6×32/(1/3) = 576

assuming  x to be the displacement form equilibrium;

Then;

[tex]F = 27sin 4t-3cos4t +k(x+1/3) - mg -3v[/tex]

(since F(t)=27sin 4t-3cos4t somehow faces downwards, mg=downwards and k(x+1/3)= upwards and medium resistance 3v =  upwards)

SO;

[tex]d2x/dt2 = 27sin 4t-3cos4t +kx - 3dx/dt[/tex]

[tex]d2x/dt2 +3dx/dt - 576x = 27sin 4t-3cos4t[/tex]

Assuming : [tex]x = asin4t + bcos4t[/tex]

[tex]dx/dt = 4acos4t - 4bsin4t[/tex]

[tex]d2x/dt2 = -16asin4t - 14bcos4t[/tex]

replacing  these values in the above equation

[tex]= -16asin4t - 14bcos4t + 12acos4t - 12bsin4t -576asin4t-576bcos4t = 27sin 4t-3cos4t[/tex]

[tex]= sin4t (-592a-12b) + cos4t(12a -590b) = 27sin 4t-3cos4t[/tex]

equating sin and cos terms

a = - 0.046 ;  b = 0.006

displacement x = - 0.046sin4t +0.006cos4t

Answer:

150(10s + h)

Step-by-step explanation:

We need to write an expression for the total items they shipped.

Let each skateboard be s.

Let each helmets be h.

The factory ships 100 boxes with 15 skateboards in each box. That is:

100 * (15 * s) = 1500s

The factory ships 10 boxes with 15 helmets in each box. That is:

10 * (15 * h) = 150h

The total number of items shipped is therefore:

1500s + 150h = 150(10s + h)

This expression represents the total number of items shipped.

Answer:

S, Z, F

Step-by-step explanation:

i know its not the question but its for anyone who found this and needs it for edge lol

Answer:

Average speed v = 24.29 mph

Total time taken ∆t = 7 hours

Step-by-step explanation:

Given;

the first 2 hours, they travel at a rate of 25 miles per hour

t1 = 2 hours

v1 = 25 mph

then take a break for 2 hours and do not travel during that time

t2 = 2 hours

v2 = 0

They finally travel again for another 3 hours at a rate of 40 miles per hour before stopping for the day.

t3 = 3 hours

v3 = 40 mph

Total time taken ∆t = sum of time taken for the day travel

∆t = t1 + t2 + t3

Substituting the values;

∆t = 2 + 2 + 3 = 7 hours

The average speed v = total distance travelled/total time taken

v = d/∆t .......1

Total distance travelled d = Σ(velocity × time)

d = v1t1 + v2t2 + v3t3

d = 25 × 2 + 0×2 + 40 × 3

d = 50 + 0 + 120

d = 170 miles

Substituting into equation 1.

v = 170 miles ÷ 7 hours

Average speed v = 24.29 mph

Answer:

b = 0

Step-by-step explanation:

Because the line passes through x values when y = 0, it means that the line is y = 0. The slope would be 0, and because we are given 2 coordinates we can determine that the y intercept would be at 0.

Answer:

c

Step-by-step explanation:

hope this helps i just had this question on edge 2020

Answer:

  108

Step-by-step explanation:

We can rewrite f(x+2) to make it easier to evaluate:

  f(x+2) = (6x +5)x -8

Since we want f(6), we want x+2 = 6, or x=4.

  f(6) = (6·4 +5)·4 -8 = 29·4 -8

  f(6) = 108

Answer:

Null hypothesis:[tex]p\leq 0.3[/tex]  

Alternative hypothesis:[tex]p > 0.3[/tex]  

Critical value: [tex] z_{\alpha/2}= 1.64[/tex]

Test statistic: [tex]z=\frac{0.462 -0.3}{\sqrt{\frac{0.3(1-0.3)}{65}}}=2.85[/tex]  

For this case the calculated value is higher than the critical value so then we can reject the null hypothesis. And we can conclude that the true proportion of cars with emissions systems which failed to meet pollution control guidelines for this case is significantly higher than 0.30 or 30%

Step-by-step explanation:

Information given

n=65 represent the random sample taken

X=30 represent the number of cars with emissions systems which failed to meet pollution control guidelines

[tex]\hat p=\frac{30}{65}=0.462[/tex] estimated proportion of cars with emissions systems which failed to meet pollution control guidelines

[tex]p_o=0.30[/tex] is the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true proportion for this case is higher than 0.3 or no, the system of hypothesis are:  

Null hypothesis:[tex]p\leq 0.3[/tex]  

Alternative hypothesis:[tex]p > 0.3[/tex]  

The statistic for this case would be:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{0.462 -0.3}{\sqrt{\frac{0.3(1-0.3)}{65}}}=2.85[/tex]  

The critical value for this case would be taking in count the significance level in the right tail:

[tex] z_{\alpha/2}= 1.64[/tex]

For this case the calculated value is higher than the critical value so then we can reject the null hypothesis. And we can conclude that the true proportion of cars with emissions systems which failed to meet pollution control guidelines for this case is significantly higher than 0.30 or 30%

Answer:

6x + y = 38.75

x + 2y = 17

price of drink is $5.75

Step-by-step explanation:

Let the price  of popcorn be x

Let the price  of drink be y.

price  of  12 bags of popcorn will be 12x

price  of  2 drinks  will be 2y

it is given that "Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks."

thus

12x + 2y = 77.50

dividing LHS and RHS by 2 we have

12x/2 + 2y/2 = 77.50/2

=> 6x + y = 38.75 _________(1)

__________________________________________________

price  of  3 bags of popcorn will be 3x

price  of  6 drinks  will be 6y

it is given that "Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks."

thus

3x + 6y = 51.00

dividing LHS and RHS by 3 we have

3x/3 + 6y/3 = 51/3

=> x + 2y = 17   _____________(2)

__________________________________________________

Thus we have two equation

6x + y = 38.75 _________(1)

x + 2y = 17

=> x = 17 - 2y

putting this value of x in equation 1 we have

6( 17 - 2y) + y = 38.75

=> 102 - 12y + y = 38.75

=> 102 - 11y = 38.75

=> -11y = 38.75 -102

=> -11y = -63.25

=> y = -63.25/-11 = 5.75

as we have x = 17 - 2y

using 5.75 in place of y

x = 17 - 2(5.75 )

=> x = 17 - 11.5

=> x = 5.5

Thus, system of equations are

6x + y = 38.75

x + 2y = 17

price of drink is $5.75

Answer:

$2668.63

Step-by-step explanation:

If the average of 4 months is $5

Meaning the total sum for 4 months

4×5 =$20

If the average for the year was $1780.75​

It means the total sum for a year is;

$1780.75​×12 =$21369

This means the money received for the remaining 8 months is;

$21369-$20=$21349

Hence the average income for the remaining 8months is ;

The total amount for 8 months / 8;

$21349/8= $2668.625

$2668.63

Answer:

I couldn't find the link you wanted me to click.

Anyway the Pyramid Volume Formula is

Volume= (Area of the Base * Height) ÷ 3

It's hard to determine the volume because I can't tell the dimensions from the graphic.

I'd guess the answer to question 4 is "A" means area of the base

Step-by-step explanation:

Answer:

[tex]t=\frac{25.3-24.5}{\frac{5.4}{\sqrt{40}}}=0.937[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=40-1=39[/tex]  

And the p value would be given by:

[tex]p_v =P(t_{(39)}>0.937)=0.177[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X=25.3[/tex] represent the sample mean

[tex]s=5.4[/tex] represent the sample standard deviation

[tex]n=40[/tex] sample size  

[tex]\mu_o =24.5[/tex] represent the value to verify

t would represent the statistic  

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean is higher than 24.5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 24.5[/tex]  

Alternative hypothesis:[tex]\mu > 24.5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{25.3-24.5}{\frac{5.4}{\sqrt{40}}}=0.937[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=40-1=39[/tex]  

And the p value would be given by:

[tex]p_v =P(t_{(39)}>0.937)=0.177[/tex]  

Answer:

[tex]x= 30/7[/tex]

Step-by-step explanation:

[tex]2/3 x = -1/2 x + 5[/tex]

[tex]2/3x+1/2x = + 5[/tex]

[tex]7/6x=5[/tex]

[tex]x=5 \times 6/7[/tex]

[tex]x= 30/7[/tex]