Caitlan went to the store to buyschool clothes . She has store credit from a previous return in the amount 39.58. If she bought 4 of the same style shirt in different colors and spent total of 52.22 after the store credit was taken off he total, what was the price of each shirt ahe bought? Write and solve and equation with integrr coefficients

Answer:

Option B is correct.

Rotation matrix = [tex]\begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}[/tex]

Step-by-step explanation:

Given a vector : [tex]<1 , 4>[/tex] , rotation by [tex]\frac{2\pi}{3}[/tex] radian.

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

The standard rotation matrix is given by;

R = [tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex]

Then, the matrix of rotation by [tex]\frac{2\pi}{3}[/tex] radian  is:

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix}[/tex] = [tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex] [tex]\begin{bmatrix}x \\ y\end{bmatrix}[/tex]

Then; substitute [tex]\theta = 120^{\circ}[/tex]

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix}\cos 120^{\circ} & -\sin 120^{\circ} \\ \sin 120^{\circ} & \cos 120^{\circ}\end{bmatrix}\begin{bmatrix}1 \\ 4 \end{bmatrix}[/tex]

or

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix} -0.5 & -0.866 \\ 0.866 & -0.5 \end{bmatrix}\begin{bmatrix}1 \\ 4 \end{bmatrix}[/tex]

or

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix} -0.5 +4(-0.866) \\ 0.866+4(-0.5)\end{bmatrix}[/tex]

Simplify:

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix} = \begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}[/tex]

Therefore, the rotation matrix of a given vector is, [tex]\begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}[/tex]

The matrix that represents the rotation of the vector 1,4 by 2pi/3 radians is : (B) [tex]\left[\begin{array}{ccc}-3.96\\-1.13\\\end{array}\right][/tex]

A matrix can be defined as a rectangular array of numbers table of numbers, symbols, or expressions that are arranged into column and rows.A matrix can take different forms which gave rise to the types of matrices.

Given that standard rotation matrix is expressed as :

[tex]R = \left[\begin{array}{ccc}cos\beta &-sin\beta \\sin\beta &cos\beta \\\end{array}\right][/tex]

therefore the matrix by rotation of [tex]\frac{2\pi }{3}[/tex]

[tex]\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}cos\beta &-sin\beta \\sin\beta &cos\beta \\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]

substituting the value of [tex]\beta = 120^o[/tex]

[tex]\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}-0.5 &+4(-0.866) \\0.866 &+4(-0.5) \\\end{array}\right] \left[\begin{array}{ccc}\\\\\end{array}[/tex]

Therefore the rotation of the vector is

[tex]\left[\begin{array}{ccc}-3.96\\-1.13\\\end{array}\right][/tex]

In conclusion, The matrix that represents the rotation of the vector 1,4 by 2pi/3 radians is : (B).

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Answer:

The correct answer option is: [tex]S_9=\frac{9}{2} (2+26)[/tex]

Step-by-step explanation:

We know that,

the sum of the first [tex]n[/tex] terms of an Arithmetic Sequence is given by:

[tex]S_9=\frac{n(a_1+a_n)}{2}[/tex]

where [tex]n[/tex] is the number of terms,

[tex]a_1[/tex] is the first term of the sequence; and

[tex]a_n[/tex] is the first term of the sequence.

So for [tex]a_n=3n-1[/tex],

[tex]a_1=3(1)-1=2[/tex]

and

[tex]a_9=3(9)-1=26[/tex]

Putting these values in the formula to get:

[tex]S_9=\frac{9(a_1+a_9)}{2}[/tex]

[tex]S_9=\frac{9(2+26)}{2} \\\\S_9=\frac{9}{2} (2+26)[/tex]

First five terms:

[tex]a_1=3(1)-1=2[/tex]

[tex]S_1=\frac{1(2+2)}{2}[/tex]=2

[tex]a_2=3(2)-1=5[/tex]

[tex]S_2=\frac{2(2+5)}{2}[/tex]=7

[tex]a_3=3(3)-1=8[/tex]

[tex]S_2=\frac{3(2+8)}{2}[/tex]=15

[tex]a_4=3(4)-1=11[/tex]

[tex]S_4=\frac{4(2+11)}{2}[/tex]=26

[tex]a_5=3(5)-1=14[/tex]

[tex]S_5=\frac{5(2+14)}{2}[/tex]=40

Answer: the corrrect one is A s9=9/2(2+26)

Answer:

(16)

Given the statement: Elmwood st. and oak Dr. are the same distance.

All intersection are perpendicular.

To prove that: Peach Dr. tree is the same distance as Sycamore Ln.

It given that all the intersection are perpendicular which means each interior angles are of [tex]90^{\circ}[/tex]

By rectangle properties:

Since, Elmwood st. and oak Dr. are the same distance.

then, by rectangle properties;

Peach Dr. tree is the same distance as Sycamore Ln            proved!

6.10

(11)

Given: [tex]\angle A \cong \angle T[/tex] , [tex]\overline{MA} \cong \overline{HT}[/tex]

To prove: [tex]\triangle MAX \cong \triangle HTX[/tex]

In ΔMAX and ΔHTX

[tex]\angle A \cong \angle T[/tex]    [Angle]               [Given]

[tex]\overline{MA} \cong \overline{HT}[/tex]      [Side]     [Given]

Vertical angle theorem states that angles that are opposite each other.

Since, these angles are formed when two lines cross each other.

And also vertical angles are congruent to each other.

Since,  [tex]\angle MXA[/tex] , [tex]\angle HXT[/tex]  are vertical angles

[tex]\angle MXA \cong \angle HXT[/tex]      [Vertical angles are congruent]

AAS (Angle-Angle-Side) theorem states that if two angles and a non-included side in one triangle are congruent to two corresponding angles and a non-included side in another triangle, then those triangles are congruent.

Then, by AAS theorem,

[tex]\triangle MAX \cong \triangle HTX[/tex]

(14)

Given: [tex]\overline{AX} \cong \overline{TX}[/tex] , [tex]\angle A \cong \angle T[/tex]

Prove that:  [tex]\overline{MX} \cong \overline{HX}[/tex]

In [tex]\triangle MXA[/tex] and [tex]\triangle HXT[/tex]

[tex]\overline{AX} \cong \overline{TX}[/tex]   [Side]          [Given]

[tex]\angle A \cong \angle T[/tex]       [Angle]                  [Given]

[tex]\angle MXA \cong \angle HXT[/tex]      [Vertical angles are congruent]

ASA (Angle -Side-Angle) theorem states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then these triangles are congruent.

then by ASA theorem;

[tex]\triangle MAX \cong \triangle HTX[/tex]

CPCT [Corresponding Part of Congruent triangles are congruent.]

⇒[tex]\overline{MX} \cong \overline{HX}[/tex] [By CPCT]        proved!

Question: if a parabola never touches the x axis, then it doesn't have any real roots or solutions

Answer: True

A real solution only occurs if the graph touches or crosses  the x axis, as the x intercept (or root) is a visual indication of a real number solution. In this case, we have 2 complex solutions for the parabola

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Question: What number is equivalent to sqrt(-49) ?

Answer: choice A) 7i

Simplify as follows

sqrt(-49) = sqrt(-1*7^2)

sqrt(-49) = sqrt(-1)*sqrt(7^2)

sqrt(-49) = i*7

sqrt(-49) = 7i

note: be careful not to toss in -7i as one of the answers, because it's not. The square root of a number is exactly one output. For instance, if you take the square root of 25, the result is 5 (not plus or minus 5).

Answer:

4

Step-by-step explanation:

theres only 4 to pick from

Answer:

Option b is correct.

Linear function ;

y =2x

Step-by-step explanation:

The formula y=f(x)=mx +c  ......[1]  is said to be a linear function. That means the graph of this function will be a straight line on the (x, y) plane, where m represents slope and b is the y-intercepts.

Consider any points from the table;

(1, 2) and (2, 4)

substitute these point in [1] we get;

for (1, 2)

⇒x = 1 and f(x) = 2 we have

2 = m + c      

or

c = 2- m                       ......[1]

for (2, 4) we have;

4 = 2m + c                       .....[2]

Now, substitute equation [1] into [2] we get;

4 = 2m + 2 -m

Combine like terms;

4 = m + 2

Subtract 2 from both sides we get;

4 -2 = m +2 -2

Simplify:

2 = m or

m = 2

Substitute the value of m = 2 in [1] to solve for c;

c = 2 -2 = 0

c =0

⇒ y = 2x +0

y = 2x

therefore, the data in the table represents the Linear function and a possible formula for the linear function is; y = 2x

Answer:

Option B. y = 2x

Step-by-step explanation:

The given table in the question is

x      0       1       2       3      4      

f(x)   0       2      4       6      8

As we know if the function is exponential or in the form of [tex]f(x) = (a)^{x}[/tex] then for x  = 0 value of this exponential function will be f(0) = 1 but as per table f(0) = 0, so the given function is not an exponential function.

Therefore the given function is a linear function.

Linear function is always in the form of y = mx + c

Now f(0) = m×0 + c = 0

c = 0

f(1) = m×1 = 2

m = 2

Now we replace the values of m and c in y = mx + c

The equation will be y = 2x.

Option B. y = 2x is the answer.

Final answer:

The test statistic for the hypothesis test regarding the proportion of veterinary clinics that do not treat large animals is approximately 5.11, calculated using the formula for the test statistic of a proportion.

Explanation:

The student is asking about calculating a test statistic for a hypothesis test concerning the proportion of veterinary clinics that do not treat large animals such as cows and horses. The proportion as per the American Veterinary Medical Association's belief is 0.5, and the survey conducted has resulted in 88 out of 120 clinics stating they do not treat large animals. To find the test statistic, we can use the formula for the test statistic of a proportion:

Test Statistic (Z) = (p - P₀) / √(P₀(1 - P₀)/n), where p is the sample proportion, P₀ is the null hypothesis proportion, and n is the sample size.

In this case:

p = 88/120

P₀ = 0.5 (as per the hypothesis)

n = 120

Substituting these values, we get:

Z = (88/120 - 0.5) / √(0.5 * (1 - 0.5) / 120) = (0.7333 - 0.5) / √(0.25 / 120) = 0.2333 / √(0.0020833) = 0.2333 / 0.04564 ≈ 5.11

Therefore, the test statistic is approximately 5.11, when rounded to two decimal places.

Answer:

The correct answer option is [tex]f(x)=-\frac{1}{2} x+3[/tex].

Step-by-step explanation:

We will take easy (clear) points on the graph i.e. (0, 3) and (6, 0) and use them to find the equation of the line given on the graph.

To find the slope:

Slope = [tex]\frac{0-3}{6-0} =-\frac{1}{2}[/tex]

Putting the values of the coordinates of one of the chosen points and slope of the line in the standard form of equation of a line to find the y-intercept (c).

[tex]y=mx+c[/tex]

[tex]3=-\frac{1}{2} (0)+c\\\\c=3[/tex]

So the equation of the graphed line in terms of f(x) will be:

[tex]f(x)=-\frac{1}{2} x+3[/tex]

A, B,  C, and E are not polynomials.

A polynomial is an expression involving exponents, constants, and variables, so long as:

You are not dividing by a variable.

You are not raising a variable to a power of a negative number.

You are not raising a variable to a power of a fraction.

You are not taking the root of a variable.

Only one of these satisfies the criteria for a polynomial, and that is D. However, the 2nd term, 0x^2 is an unnecessary term, and would only be included if dividing this polynomial by another polynomial.

Solution:

[tex]\frac{1}{2}\times-4 \frac{4}{5}[/tex]

As one of the fraction is a proper fraction and another one is Mixed fraction.

There are two methods of solving it.

1. [tex]\frac{1}{2}\times-4 \frac{4}{5}=\frac{1}{2} \times \frac{-24}{5}=\frac{-12}{5}=-2\frac{2}{5}[/tex]

2. [tex]\frac{1}{2}\times-4 \frac{4}{5}=\frac{1}{2}[-4-\frac{4}{5}]=\frac{1}{2}\times (-4)+\frac{1}{2}\times\frac{-4}{5}=-2+\frac{-2}{5}=\frac{-10-2}{5}=\frac{-12}{5}=-2\frac{2}{5}[/tex]→→Here i have used Distributive property with respect to addition and Subtraction i.e a×(b+c)= a ×b + a×c or a×(b-c)=a×b-a×c

Now, you can fill the blanks by yourself.

Answer:Barbara writes each number as a fraction and then multiplies.

-24/5 -12/5

Answer:Christopher writes the mixed number as a sum and uses the distributive property.

-4 -4/5 -2 -2/5

Answer:Barbara's and Christopher’s answers will be equal. Write the answer as a mixed number in simplest form.

-2 2/5

Step-by-step explanation:

Answer:

Hey,

your answer is   56cm^2

Answer:

15.4 gallons .

Step-by-step explanation:

The rate of gas used  = 380/14 = 27.14 gallons per gallon.

So for each gallon used  you drive 27.14 miles.

So number of gallons used when travelling 418 miles = 418/27.14

= 15.4 gallons .

At the rate your car consumes gas, you will need 15.4 gallons to drive 418 miles.

The first thing to do here is to find out how many miles you can go with a single gallon of gas.

= Gas used / Number of miles traveled

= 14 / 380

= 0.0368 gallons per mile

Now that you have to drive 418 miles, the amount of gas you will need is:

= Number of miles to travel gas per mile

= 418 x 0.0368

= 15.4 gallons

In conclusion, you will need 15.4 gallons.

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Answer: 3996 meters

Step-by-step explanation:

Given: Maya is camping at the top of mount armstrong at an elevation of 7832 meters.

Consider the pont of sea level be 0.

Then the  height of the point where Mary is = +7832 meters (by using integers)

Juan is scuba diving 160 meters below sea level.

⇒The height of the point where Juan is =-160 meters

The distance between them =[tex]7832-(-160)=7832+160=7992\ meters[/tex]

The mid point of the distance= [tex]\frac{1}{2}\times7992=3996\ meters[/tex]

Hence, Maya & Juan meet will meet at an elevation of 3996 meters .

Final answer:

Maya and Juan will meet at an elevation of 3836 meters.

Explanation:

To find the elevation at which Maya and Juan will meet, we need to calculate the average of their elevations. Maya is at an elevation of 7832 meters and Juan is at an elevation 160 meters below sea level. The average of these two elevations is:

Average = (7832 + (-160)) / 2 = 3836 meters.

Therefore, Maya and Juan will meet at an elevation of 3836 meters.

Answer: B

Step-by-step explanation:

  3x³ - 7x² +  0x + 12       →          3x³ - 7x² +  0x + 12

- (3x³ + 6x² + 10x + 0)      →    +   (-3x³ - 6x² - 10x - 0)

                                                            -13x²  - 10x  + 12

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have the line in point-slope form:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\y-2=\dfrac{7}{3}(x+5)\to m_1=\dfrac{7}{3}\\\\\text{therefore}\ m_2=-\dfrac{1}{\frac{7}{3}}=-\dfrac{3}{7}.\\\\\text{We have the slope}\ m=-\dfrac{3}{7}\ \text{and the point}\ (-4,\ 9).\ \text{Substitute:}\\\\y-9=-\dfrac{3}{7}(x-4))\\\\\boxed{y-9=-\dfrac{3}{7}(x+4)}[/tex]

Answer:

from ride one to two its 300 then from two to three its 400 then from three to four its 300 then from four to three its 300.

so add it all up

300 + 300 + 300 + 400 = 1,300 yards and that is you answer

hope i helped and have a good day!

Answer:

y = x + 20

Step-by-step explanation:

Isolate the variable you are solving for, y. Note the equal sign, what you do to one side, you do to the other. Add 20 to both sides

x (+20) = y - 20 (+20)

y = x + 20

y = x + 20 is your answer

Answer: Y= x+20

Step-by-step explanation: x = y-20, you must first add 20 to both sides to get Y on its own. So x+20 = y - 20 + 20, the twenties cancel each other out giving us x+20 = y or y=x+20

Answer:

Tyler's height in centimeters is, 144.78 centimeters.

Step-by-step explanation:

Given the statement: Tyler's height is 57 inches.

To find his height in centimeters.

Using the conversion:

[tex]1 {\tex}inch = 2.54 {\tex}centimeters[/tex]

Proportion states that the two ratios or fraction are equal.

Using proportion method:

[tex]\frac{1}{57} = \frac{2.54}{x}[/tex]

By cross multiply, we get

[tex]x = 57 \times 2.54 = 144.78[/tex] centimeters.

therefore, his height in centimeter is, 144.78 inches.

To convert Tyler's height from inches to centimeters, we multiply his height in inches (57) by the unit conversion factor (2.54 cm/inch), giving us 144.78 cm. Thus, Tyler's height in centimeters is 144.78 cm.

The question asks: Tyler's height is 57 inches. What could be his height in centimeters?

To answer this, we need to convert inches into centimeters. We do this using a unit conversion factor, which in this case is given as 1 inch = 2.54 centimeters. Therefore, Tyler's height in centimeters would be 57 inches multiplied by 2.54 (the unit conversion factor), giving us 144.78 cm.

Here's the step-by-step calculation:

So, Tyler's height in centimeters is 144.78 cm.

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Answer: 29

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

To get this answer, you subtract the largest and smallest values, which are also known as the max and min respectively

Range = Largest Value - Smallest Value

Range = Max - Min

Range = 65 - 36

Range = 29

If it helps, sort the data in order from smallest to largest to get this list of values: {36, 36, 41, 46, 50, 52, 56, 65} so you can see the min and max easier. The range is basically the spread of the data (more or less). The larger the range, the more spread out the data values are.

The range of the data set (36, 36, 41, 46,  50, 52, 56, 65) will be 29.

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.

The range of data gathering in statistics is the difference between the highest and smallest values, calculated by subtracting their sample maximum and minimum.

In a recent survey, 8 college graduates were each asked for the number of hours they work each week. Here is a list of the responses.

50, 52, 36, 46, 41, 36, 56, 65

Arrange the data in ascending order. Then we have

36, 36, 41, 46,  50, 52, 56, 65

Then the range of the data is given as,

Range = 65 - 36

Range = 29

The range of the data set  36, 36, 41, 46,  50, 52, 56, 65 will be 29.

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Answer:

55 gallons

Step-by-step explanation:

Given that the diameter of the cylindrical barrel is 22 inches, so the radius of the barrel is [tex]\frac{22}{2}=11 \text{ inches}[/tex]

And height of the cylindrical barrel is 33.5 inches.

So the volume of oil in the cylindrical barrel is

[tex]=\pi r^2 h\\=\pi (11)^2(33.5)\\\\\approx 12734.45 \text{ cubic inches}[/tex]

Also given that there are 231 cubic inches in a liquid gallon, so to find the number of gallons of oil in barrel, we use unitary method.

231 cubic inches goes in = 1 gallon

1 cubic inches will go in [tex]=\frac{1}{231} \text{ gallon}[/tex]

[tex]\text{12734.45 cubic inches oil will go in}=\frac{1}{231}\times 12734.45\approx 55.12 \text{ gallons}\\\\\text{hence there are approximately 55 gallons of oil in the barrel}[/tex]

Answer:

55

Step-by-step explanation:

Answer:

<1 and <3

Step-by-step explanation:

The pairs of angles on one side of the line but in between the other two lines are called consecutive interior angles.

<1 and <3

<2 and <6

Answer:

Probability states the ratio of number of favorable outcomes to the total number of possible outcomes.

i.e,  [tex]probability = \frac{Number of favourable outcomes }{Total number of possible outcomes}[/tex]

A bag contains:

Brown marble = 4

Green marbles = 3

Red marbles = 2

Purple marble = 1

Total number of possible outcomes = (4+3+2+1) = 10 marbles

P(Brown marbles) = [tex]\frac{4}{10}=\frac{2}{5} = 40\% = 0.4[/tex]

P(Green marbles) = [tex]\frac{3}{10} = 30\% = 0.3[/tex]

P(Red marbles) = [tex]\frac{2}{10}=\frac{1}{5} = 20\% = 0.2[/tex]

and

P(Purple marbles) = [tex]\frac{1}{10}= 10\% = 0.1[/tex]

Answer:The possible outcome would be 10, because 4 brown marbles + 2 red marbles + 1 purple marble+3 green marbles = 10 outcomes!

Step-by-step explanation:

I just did it =w=

Answer:

B. 5x - 4y = 12

Step-by-step explanation:

Let's convert this to slope-intercept form to interpret the equation easier.

5x - 4y = 12

Subtract 5x from both sides.

-4y = -5x + 12

Divide both sides by -4.

y = 5/4x - 3

Based on this, we know the slope is 5/4 and the y-intercept is (0, -3). When you count the rise over run in the picture and look at the y-intercept, they match.

Answer:

y=7

Step-by-step explanation:

We know the tops 2 parts of the kite have to be equal

x+3 = 15

Subtract 3 from each side

x+3-3 =15-3

x=12

We also know the bottoms have to be equal

3y-1 =2x-4

Substitute the value for x

3y-1 =2(12) -4

3y-1 =24-4

3y-1 =20

Add 1 to each side

3y-1+1 =20+1

3y = 21

Divide each side by 3

3y/3 = 21/3

y = 7

Answer:

Dec % = 340/1360*100= 25%

Answer:

f(5)=469

Step-by-step explanation:

To find the value of the polynomial at x=5, we substitute the value 5 in for x into the polynomial. We then simplify using PEMDAS or order of operations.

[tex]x^4-2x^3+5x^2-7x+4\\(5)^4-2(5)^3+5(5)^2-7(5)+4\\625-250+125-35+4\\375+125-35+4\\500-35+4\\465+4\\469\\f(5)=469[/tex]

Answer:

469

Step-by-step explanation:

Final answer:

To adjust the fruit punch from 50% to 70% juice, Sara needs to add 4 gallons of fruit juice to the existing 6 gallons of punch.

Explanation:

The student is attempting to adjust the concentration of juice in a fruit punch mixture from 50% to 70%. Initially, Sara has 6 gallons of punch which is 50% juice. To find out how much fruit juice should be added to reach a 70% juice mixture, we can use the equation of concentration:

Let the amount of juice to be added be x gallons. The total amount of juice in the mixture would then be 50% of 6 gallons plus x gallons, and the total volume of the mixture would be 6 gallons plus x gallons.

The equation representing the new concentration is:

(3 + x) / (6 + x) = 70/100

To solve for x, multiply both sides by (6 + x) and then by 100 to clear the percentage and denominator:

3 + x = 0.7 * (6 + x)

3 + x = 4.2 + 0.7x

Now, subtract 0.7x from both sides:

3 + 0.3x = 4.2

And then subtract 3 from both sides:

0.3x = 1.2

Divide both sides by 0.3 to solve for x:

x = 4 gallons

Therefore, Sara needs to add 4 gallons of fruit juice to the existing punch to create a mixture that is 70% juice, rounding to the nearest hundredth.