The cougars scored a total of 90 points in their basketball game last night against the bears. the cougars made no one-point shots, and a total of 40 two-point and three-point shots. let x represent the two-point shots and y represent the three-point shots.

part a
write and solve a system of equations that can be used to determine the number of two-point and three-point shots the cougars made.

part b
identify the solution​

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

x = 70

y = 110

z = 30

Step-by-step explanation:

all triangles add up to 180

30 + 80 = 110

180 - 110 = 70

x = 70

30 + 40 = 70

70 + 80 = 150

180 - 150 = 30

z = 30

40 + 30 = 70

180 - 70 = 110

y = 110

Answer:

2 × 10⁵

Step-by-step explanation:

The following data were obtained from the question:

6×10⁹/ 3×10⁴ =?

The above expression can be simplified as follow:

6×10⁹/ 3×10⁴ = 6×10⁹ ÷ 3×10⁴

Recall:

Aᵐ ÷ Aⁿ = Aᵐ ¯ ⁿ

Therefore,

6×10⁹ ÷ 3×10⁴ = (6/3) × 10⁹ ¯ ⁴

6×10⁹ ÷ 3×10⁴ = 2 × 10⁵

Thus, 6×10⁹/ 3×10⁴ is equal to 2 × 10⁵

Answer:

Eleven thousand five hundred and twenty

Step-by-step explanation:

E2021

According to the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.

It is given to us that -

Amount of time a person experiences cold virus symptoms are normally distributed with

a mean of 7.5 days

and, a standard deviation of 1.5 days

We have to find out the proportion of cold sufferers that experience symptoms for more than 8 days.

Now, from the given information, we have

Mean = μ = 7.5

Standard deviation = σ = 1.5

and, X = 8

Now, the proportion of cold sufferers that experience symptoms for more than 8 days can be represented as -

P(X > 8)

= P{[(X-μ)/σ] > [(8-7.5)/1.5]}

=P(Z>0.33)

Looking at the z-score values, we find out that

P(Z>0.33) = 0.129 = 12.9%

Thus, from the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.

To learn more about standard deviation visit https://brainly.com/question/13905583

#SPJ4

On the left I make the integral with respect to P and on the right the integral with respect to t

we use e to simplify Steps to constant

now, solve P

to find c we use P(0)=4, so when we replcae t=0 the soltuion must be 4

the complete function is

or

so, the right option is C

Answer: c. det(PAP^-1) = det(A)

To show that det(PAP-1) = det(P)det(A)det(P^-1), we can use the following properties of determinants:

1. det(AB) = det(A)det(B) for any matrices A and B

2. det(A^-1) = 1/det(A) for any invertible matrix A

Starting with det(PAP^-1), we can apply property 1 to get:

det(PAP^-1) = det(P)det(A)det(P^-1)

Then, we can use property 2 to rewrite det(P^-1) as:

det(PAP^-1) = det(P)det(A)(1/det(P))

Simplifying this expression gives:

det(PAP^-1) = det(A)

Therefore, det(PAP^-1) = det(P)det(A)det(P^-1) is equivalent to det(PAP^-1) = det(A).

So, the correct answer is:

c. det(PAP^-1) = det(A)

Answer:

c should be the answer

Step-by-step explanation:

Answer:

140 is total length.

Step-by-step explanation:

If it is square, the formula for the area of the land would equal \(x^{2}\).

Or, side times side.

So, you would have to find the square root of 1225, which is 35.

Since there is four sides, 35*4 = 140

140 is the total length of the wire.

The length of each piece is 150/3 which is 46.(6)

M∩C =  {8}

M∪C =  {6, 8, 9 , 10}

Sets can be defined as an organized collection of objects represented in set-builder form or roster form.

Sets are mostly represented in curly braces {}

For example, A = {a, b, c, d, e} is a set.

From the information given, we have that:

Thus,

M = {8, 9, 10}

C = {6, 8, 10}

M∩C = Number common in both sets

M∩C = {8}

M∪C = Combinations of numbers in both sets without repetition

M∪C =  {6, 8, 9 , 10}

Thus, the value of M∩C is 8 and that of M∪C is 6, 8, 9, 10

Learn more about sets here:

https://brainly.com/question/2166579

#SPJ1

Answer: number 2 is a obtuse angle and number 3 is a right angle

The area of the parallelogram in the given diagram is 103.68 cm²

From the question, we are to determine the area of the given parallelogram

The area of a parallelogram can be calculated by using the formula,

A = bh

Where A is the area

b is the base

and h is the perpendicular height

From the given diagram,

b = 14.4 cm

h = 7.2 cm

Putting the parameters into the equation, we get

A = 14.4 × 7.2

A = 103.68 cm²

Hence, the area of the parallelogram in the given diagram is 103.68 cm²

Learn more on Calculating area of Parallelogram here: https://brainly.com/question/22685859

#SPJ1  

Answer:

To convert an improper fraction to a mixed fraction, divide the numerator by the denominator, write down the quotient as the whole number and the remainder as the numerator on top of the same denominator. Let us see an example of this conversion

Step-by-step explanation:

Convert 23/4 into a mixed fraction

Answer:

linear graph

Step-by-step explanation:

if the points are coming in a straight line it is linear

Answer:

42.84 cm

Step-by-step explanation:

It would be easiest to split this first. To find the circumference of a circle, it is 2πr.

d= 12

r= 6

C= 2π6

C= 12π

Divide by 2 because you are only trying to get the circumference of half the circle.

C= 6π

Now you can add all the other sides to find the total perimeter.

P= 6(3.14) + 10 + 6 + 8

P= 42.84 cm

Answer:

61.68cm

Step-by-step explanation:

semicircle=12x2x3.14x1/2=37.68

trapezium=10+6+8=24

s+t=61.68cm

Answer:

did u find the answers to all of that quiz if u did can u tell me the right answers

Step-by-step explanation:

The area of the figure is given as follows:

100.56 mm².

The figure in this problem is composed as follows:

The areas for each region are given as follows:

Hence the total area is of:

48 + 14 + 20 + 6 + 12.56 = 100.56 mm².

More can be learned about area at https://brainly.com/question/15673093

#SPJ1

Answer: A.

Step-by-step explanation:

This is the only option in which the terms are ordered from least to greatest.

Therefore, A is the correct answer.

The superposition is the imposing of one wave on the other and resulting in the change of the amplitude of the final wave.

When two or more waves travel through the same space in superposition, their combined amplitudes equal the amplitudes they would have produced individually. For instance, two waves moving in the same direction will pass through each other without causing any distortion on the other side.

The pattern you see when shining light through two slits, the sounds you hear in acoustically sound rooms and music halls, the interference radios receive when moved close to other electronic devices, and any tone produced by a musical instrument are all examples of the superposition principle in action.

To know more about superposition, visit,

https://brainly.com/question/29518396

#SPJ4

Answer:

c=5.87g

Step-by-step explanation:

because you know c is total cost and g is grams. 5.87g would be the cost per gram multiplied by the number of grams you need.

The number of green beads left over = 15

Walter:

Number of green beads = 476

Number of red beads = 32

Agnes:

Number of green beads = 104

Number of red beads = 16

Holly:

Number of green beads = 281

Number of red beads = 80

Total number of red beads = 32+16+80 = 128 beads

Number of red beads required for making one lizard = 16

Since 128/16 = 8 , there will be no red beads left after making 8 lizards.

Total number of green beads = 476+104+281 = 861 beads

Number of green beads required for making one lizard = 94

Now 861/94 = \(9\frac{15}{94}\)

That is , 15 is the remainder when 861 is divided by 94

So there will be 15 green beads left after making 9 lizards.

Therefore, the number of green beads left over = 15

Learn more remainder problems at https://brainly.com/question/14462792

#SPJ4

No, Malik's mixed number 63 5/6 is not correct as the answer to the problem was 33 5/6.

A mixed number is a number that consists of a whole number and a fraction. In Malik's answer, 63 is the whole number and 5/6 is the fraction. The mixed number 33 5/6 means that Malik got 33 full wholes and 5 out of 6 parts of another whole.

A mixed number is one that includes both a proper fraction and a full number.

​Therefore, Malik's answer is incorrect and his mixed number 63 5/6 does not match the correct answer of 33 5/6.

Learn more about mixed number here :

brainly.com/question/24137171

#SPJ4

The scale Denise used is as follows:

3 centimetres: 2 metres

Denise measured a community college and made a scale drawing. In real life, at the college is 122 meters long. it is 183 centimetres long in the drawing.

The scale of Denise use can be calculated as follows:

Using the proportional relationship,

3 / x = 183 / 122

cross multiply

122(3) = 183x

366 = 183x

divide both sides by 183

x = 366 / 183

x  = 2 metres.

learn more on scale here: https://brainly.com/question/32042187

#SPJ4

"a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years.

The 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].According to the central limit theorem , a sampling distribution of the means is usually distributed in a normal distribution, given a big enough sample size, which means that it has a bell-shaped curve. It has a standard deviation that can be estimated by dividing the population standard deviation by the square root of the sample size. Using the formula below,

we can calculate the 95% confidence interval for the population average.= 13.8 ± (1.96 × 7.3 / √45)

= 13.8 ± (1.96 × 1.088)

= 13.8 ± 2.13The limits are calculated by adding and subtracting the calculated value from the sample mean.13.8 + 2.13

= 15.9313.8 - 2.13

= 11.67Therefore, the 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].

To know more about average, visit:

https://brainly.com/question/24057012

#SPJ11

Answer:

this is not originally by me

Step-by-step explanation:

10t = b - 4

12b+8t = $348

This is a system of equations. I’ll be solving through substitution.

In the first equation. solving for b (the easier variable to isolate) gives you:

b = 10t + 4

Substitute this into the second equation:

12(10t+4) +8t = 348

120t+48+8t = 348

128t = 300

t = 2.34375 —> round it to the nearest cent to get 2.34 dollars

b = 10t+4

b = 10(2.34)+4

b = 27.4 dollars

The p-value is 0.15 which is greater than the significance value 0.10 so null hypothesis cannot be rejected at 10% significance level , we do not have enough evidences to state that no- show rate is less than 6%.

As given in the question,

Null hypothesis : No show rate for passengers booked on given flight is 6%

Alternative hypothesis: No show rate  for passengers booked on given flight  is less than the 6%

P = 6%

  = 0.06

1 -  P = 1 - 0.06

       = 0.94

random sample size 'n' = 380

no shows = 18

Sample proportion 'p' = 18/ 380

                                    = 0.047

Now , z test statistic value :

z = (p - P)/ √P (1- P)/n

 = (0.047 - 0.06)/√0.06( 0.94)/380

 = -0.013 /0.012

 = -1.083

p-value = 0.2788 ( using table)

0.2788 > 0.10

p-value is greater than significance value 0.10

Do not reject null hypothesis at 10% level of significance.

Therefore, as p-value is greater than significance value do not have enough evidences to state that no- show rate is less than 6%.

Learn more about p-value here

brainly.com/question/14790912

#SPJ4

The equation to model the cost of making different numbers of shirts is c = 7.50t - 750.

Y = mx + b, where x is the independent variable, m is the slope, and b is the y-intercept, is the slope-intercept form of a linear equation. The dependent variable's rate of change with respect to the independent variable is represented by the slope (m), and its value when the independent variable is zero is shown by the y-intercept (b).

This equation's form is helpful for charting linear functions since the slope and y-intercept provide information about the direction and steepness of the line as well as its point of intersection with the y-axis.

The linear equation is given by the formula:

y = mx + b

Here. m is the slope.

The value of m is given as:

m = (y2 - y1) / (x2 - x1)

Substituting the points 100, 600) and (250, 1387.50) from the table:

m = (1387.50 - 600) / (250 - 100)

m = 7.50

Now, for the y-intercept b we have:

b = y - mx

Substituting the data point:

b = 600 - 7.50(100)

b = -750

Now the equation of the model is:

c = 7.50t - 750

Hence, the equation to model the cost of making different numbers of shirts is c = 7.50t - 750.

Learn more about slope-intercept form here:

https://brainly.com/question/29146348

#SPJ1

Based on the equation in the question , the R2 would be 0.934.

To compute R2, we need to use the formula:

R2 = SSR / SST

Given that SSR = 14,141.7 and

SST = 15,128.4,

We can substitute these values into the formula:

R2 = 14,141.7 / 15,128.4

R2 ≈ 0.934

b. To compute Ra2, we need to subtract R2 from 1:

Ra2 = 1 - R2

Substituting the value of R2 we calculated in part a:

Ra2 ≈ 1 - 0.934

Ra2 ≈ 0.066

c. A large R2 value indicates that the estimated regression equation explains a large amount of the variability in the data.

In this case, R2 is approximately 0.934, which means that the estimated regression equation explains about 93.4% of the variability in the data.

So, the answer is "Yes".

To know more on Regression visit:

https://brainly.com/question/32505018

#SPJ11

Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).