Elena went to a sporting goods store that was having a
sale. She bought one tennis racket for $43 and tennis
balls for $15. Everything she bought was on sale for
5% and there was a tax of 8.5%.
How much did Elena pay for everything?

Answer:

x = -1/2, 3/4

Step-by-step explanation:

Step 1: Factor

(2x + 1)(4x - 3) = 0

Step 2: Find roots

2x + 1 = 0

2x = -1

x = -1/2

4x - 3 = 0

4x = 3

x = 3/4

==========================================================

Explanation:

m = number of men

w = number of women

The ratio of men to women is 7 to 5, meaning that m/w = 7/5

Cross multiply to get 5m = 7w.

Then divide both sides by 5 to end up with m = 7w/5 which is the same as m = 1.4w

We'll use this equation later.

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

Since there are 336 total workers, we know that:

m+w = 336

1.4w+w = 336 .... replace m with 1.4w

2.4w = 336

w = 336/(2.4)

w = 140 women work at the company

and m = 1.4*w = 1.4*140 = 196 men work at the company as well.

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

Checking the answer:

m+w = 196+140 = 336

m/w = 196/140 = (7*28)/(5*28) = 7/5

This helps confirm we have the correct value of w.

Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

Step-by-step explanation:

1) the temperature rise, because 8.5 is C higher than 0 C

2) 8.5 - 0 = 8.5

So it rised by 8.5 degrees ( to know how many dgrees is is rised subtract the second number from the first number)

Answer:

\(m\angle 2=95^{\circ}\)

Step-by-step explanation:

It is given that ∠1 and ​∠2​ are a linear pair. So, there sum is 180 degrees.

\(m\angle 1+m\angle 2=180^{\circ}\)    ...(1)

∠2​ and ​∠3​ are vertical angles. So, both are equal.

\(m\angle 2=m\angle 3\)     ...(2)

From (1) and (2), we get

\(m\angle 1+m\angle 3=180^{\circ}\)

Substitute \(m\angle 1=(3y+10)^{\circ}\) and \(m\angle 3=(5y-30)^{\circ}\) in the above equation.

\((3y+10)^{\circ}+(5y-30)^{\circ}=180^{\circ}\)

\((8y-20)^{\circ}=180^{\circ}\)

\(8y-20=180\)

\(8y=180+20\)

Divide both sides by 8.

\(y=\dfrac{200}{8}\)

\(y=25\)

The value of y is 25.

Using equation (2), we get

\(m\angle 2=m\angle 3=(5y-30)^{\circ}\)

Substitute y=25.

\(m\angle 2=(5(25)-30)^{\circ}\)

\(m\angle 2=(125-30)^{\circ}\)

\(m\angle 2=95^{\circ}\)

Therefore, \(m\angle 2=95^{\circ}\).

Answer:

$11.50

Step-by-step explanation:

15% of 10 is 1.5

10-1.5=8.5

20-8.5=11.5

a. Im(Mu) = Im(Mu + iMv)

=> 0 = bv - aiv

=> Mv = -bu + av

b. G^-1MG is equivalent to the standard rotation-dilation matrix Ca,b.

a. We have the complex eigenvector u + iv with eigenvalue a - bi. By applying the matrix M to this eigenvector, we get:

Mu = M(u + iv) = Mu + iMv

Since M is a real matrix, the real and imaginary parts must be equal:

Re(Mu) = Re(Mu + iMv)

=> Mu = au + biv

Similarly,

Im(Mu) = Im(Mu + iMv)

=> 0 = bv - aiv

=> Mv = -bu + av

b. Let's consider the matrix G = [u | v], where the columns are u and v in that order. Multiplying this matrix by M, we have:

MG = [Mu | Mv] = [au + bv | -bu + av]

On the other hand, let's compute GCa,b:

GCa,b = [u | v] Ca,b = [au - bv | bu + av]

Comparing these two expressions, we can see that MG = GCa,b.

c. To show that u and v are linearly independent, we assume that there exist real numbers r and s such that ru + sv = 0. Applying the matrix M to this equation, we get:

0 = M(ru + sv) = rMu + sMv

0 = r(au + bv) + s(-bu + av)

0 = (ar - bs)u + (br + as)v

Since u and v are complex eigenvectors with distinct eigenvalues, they cannot be proportional. Therefore, we have ar - bs = 0 and br + as = 0. Solving these equations simultaneously, we find that r = s = 0, which implies that u and v are linearly independent.

d. Since u and v are linearly independent, the matrix G = [u | v] is invertible. Let's denote its inverse as G^-1. Now, we can show that G^-1MG = Ca,b:

G^-1MG = G^-1 [au + bv | -bu + av]

= [G^-1(au + bv) | G^-1(-bu + av)]

= [(aG^-1)u + (bG^-1)v | (-bG^-1)u + (aG^-1)v]

= [au + bv | -bu + av]

= Ca,b

Therefore, we conclude that G^-1MG is equivalent to the standard rotation-dilation matrix Ca,b.

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The particle's motion along the parabola from x = -1 to x = 2 results in a work done of 13.5 units.

To find equations of parabola we compute the work done by the force field in moving a particle along a curve, we can use the line integral formula:

Work = ∫C F · dr

where F is the force field and dr is the differential displacement vector along the curve C.

Given the force field F(x, y, z) = xi + yj + zk, and the curve defined by y = 3x² and z = 0, we need to express F and dr in terms of the parameter x.

The differential displacement vector dr can be written as:

dr = dx i + dy j + dz k

Since z is constant (z = 0), dz = 0, so dr simplifies to:

dr = dx i + dy j

We can express dy in terms of dx using the equation of the parabola

y = 3x²:

dy = 6x dx

Now we can rewrite dr as:

dr = dx i + 6x dx j

Substituting F and dr into the line integral formula:

Work = ∫C (xi + yj + zk) · (dx i + 6x dx j)

Now we calculate the dot product between F and dr:

F · dr = (xi + yj + zk) · (dx i + 6x dx j)

= x dx + 6x² dx

Integrating the dot product over the curve C from x = -1 to x = 2:

Work = ∫C (x dx + 6x² dx)

= ∫[from -1 to 2] (x + 6x²) dx

Integrating with respect to x:

Work = [1/2 x² + 2x³] | from -1 to 2

= [1/2 (2)² + 2(2)³] - [1/2 (-1)² + 2(-1)³]

= [1/2 (4) + 2(8)] - [1/2 + 2(-1)]

= 2 + 16 - 1/2 - 4

= 13.5

Therefore, the work done in moving the particle along the parabola from x = -1 to x = 2 is 13.5 units.

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The given numerical value of $44,000 represents the average salary of all assembly-line employees at a certain car manufacturer. Hence, it is a parameter.

In statistical analysis, the terms "parameter" and "statistic" are used to distinguish between population characteristics and sample characteristics, respectively. To determine whether the given numerical value represents a parameter or a statistic, we need to understand the context in which the value is used.

A parameter refers to a numerical value that describes a characteristic of a population. It represents a fixed, unknown value and is typically denoted by Greek letters. Parameters are derived from data collected from an entire population.

On the other hand, a statistic refers to a numerical value that describes a characteristic of a sample. It is computed from a subset of data, known as a sample, and is used to estimate the corresponding population parameter.

In the given statement, the average salary of all assembly-line employees at a certain car manufacturer is stated to be $44,000. Since this value represents the average salary of all employees in the population, it is a parameter. The value is derived from information about the entire population of assembly-line employees at the car manufacturer, rather than a sample.

If the statement had mentioned the average salary of a sample of assembly-line employees, then the numerical value would have been a statistic. In that case, it would have been computed from a subset of the data (a sample) and used to estimate the average salary of the entire population.

In summary, the given numerical value of $44,000 represents the average salary of all assembly-line employees at a certain car manufacturer. Hence, it is a parameter.

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The probability that your single battery-powered alarm clock works successfully when you need it is 99.5% and probability that both the battery-powered alarm clock and the smartphone alarm clock fail is 0.026%

It is a branch of mathematics that deals with the occurrence of a random event.

a. The probability that a single battery-powered alarm clock works successfully is 1 minus the probability that it fails.

1 - 0.005 = 0.995 or 99.5%.

b. The probability that both the battery-powered alarm clock and the smartphone alarm clock fail is the product of their individual probabilities of failure.

0.005 x 0.052 = 0.00026 or 0.026%.

The probability that both of them do not fail is the complement of the probability that they both fail

1 - 0.00026 = 0.99974 or 99.974%.

Hence, the probability that your single battery-powered alarm clock works successfully when you need it is 99.5% and probability that both the battery-powered alarm clock and the smartphone alarm clock fail is 0.026%

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Numbers like 10, 100, 1,000, and so on are called Powers of ten

A symbol used to denote the action of raising to a power that is written above and to the right of a mathematical phrase. Explanatory or interpreting in 2a. b: one who upholds, upholds, or demonstrates.

Powers of ten are the solution. A power of ten is equal to 10 times the exponentiation of the exponent by itself.

As an illustration, 10 = 10 * 1. 100 = 10 * 10. 1000 = 10 * 10 * 10.

The power of ten must have the same number of zeros as its exponent. For example, since 1000 includes three zeros, its exponent is three: 1000 = 103. Hope this was useful.

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Answer:

y=-27+3/5   or 138 or 5 if need as a fraction

Step-by-step explanation:

5(y+25)-(-13)=0

add all the numbers together and all the variables

5(y+25)+13=0

multiply parentheses to get

5y+125+13=0

add all the numbers together n all the variables together to

5y+138=0

Then  move all terms hat have  y to the left and terms to the right

so 125  basiclly

5y=-138

y=-138/5

y=-27+3/5  aslo could be known as  - 138 over 5 (fraction )

Answer:

True

Step-by-step explanation:

x - 4y = 11 → (1)

- 3x + 5y = 25 → (2)

Multiply (1) by 5 and (2) by 4 to eliminate the y- term

5x - 20 y = 55 → (3)

- 12x + 20y = 100 → (4)

Add (3) and (4) term by term to eliminate y

- 7x + 0 = 155

- 7x = 155 ← y- term is eliminated

The volume of the composite space figure is approximately 2818.33 cubic cm.

To find the volume of the composite space figure, we need to add the volumes of the rectangular prism and the rectangular pyramid.

The rectangular prism has a length of 26 cm, a width of 5 cm, and a height of 14 cm. So its volume is:

V_prism = length x width x height

V_prism = 26 cm x 5 cm x 14 cm

V_prism = 1820 cubic cm

The rectangular pyramid has a height of 23 cm and a rectangular base with a length of 26 cm and a width of 5 cm. To find its volume, we need to first find its base area:

A_base = length x width

A_base = 26 cm x 5 cm

A_base = 130 square cm

Then, we can use the formula for the volume of a pyramid:

V_pyramid = (1/3) x base area x height

V_pyramid = (1/3) x 130 square cm x 23 cm

V_pyramid = 998.33 cubic cm (rounded to the nearest hundredth)

To find the total volume of the composite space figure, we add the volumes of the prism and the pyramid:

V_total = V_prism + V_pyramid

V_total = 1820 cubic cm + 998.33 cubic cm

V_total = 2818.33 cubic cm (rounded to the nearest hundredth)

Therefore, the volume of the composite space figure is approximately 2818.33 cubic cm.

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Because it permits one to assume that the sampling distribution of the mean would typically be normally distributed, the central limit theorem is helpful when examining big data sets. This makes statistical analysis and inference simpler.

Hypothesis :

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

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Answer:

sorry i cant really see it

Step-by-step explanation:   poop

Answer:

I did the work and uploaded the picture i hope it helped!!

Answer:

Yes, there is enough paint to cover the table top.

Step-by-step explanation:

We are told in the above question that the table top is round = circular

The area of a circle = πr²

Diameter = 6 feet

Radius = Diameter/2 = 6 feet/2 = 3 feet

Area of the table top= π × 3²

= 28.27 square feet

We are told that the a sample jar will cover 30 square feet.

Therefore, yes, there is enough paint to cover the table top.

Answer:

43/10 pounds = 4 3/10 pounds

Step-by-step explanation:

for this you want to subtract 6 7/10 minus 2 2/5. You first have to get a common denominator and find the numerator then subtract.

Given:

The graph of system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be \(\leq\).

\(y\leq 10\).

The shaded region lies on the right side of the y-axis. So, \(x\geq 0\).

Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-1=\dfrac{2-1}{1-0}(x-0)\)

\(y=1(x)+1\)

\(y=x+1\)

The boundary line \(y=x+1\) is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be \(>\).

\(y> x+1\)

So, the required system of inequalities is:

\(y> x+1\)

\(y\leq 10\)

\(x\geq 0\)

Therefore, the correct option is B.

we have proven that point (1, √3) satisfies the equation of the circle and lies on the circle.

Theorems are what mathematics is all about. A theorem is a statement that has been proved true by a special kind of logical argument called rigorous proof.

To prove or disprove that point (1, √3) lies on the circle centered at the origin and contains point (0, 2),

we need to use the distance formula for a point (x,y) on a circle with center (a,b) and radius r:

d = √[(x - a)² + (y - b)²]

In this case, the center of the circle is (0,0)

since it's centered at the origin, and the point (0,2) lies on the circle.

We can calculate the radius of the circle using the distance formula:

r = √[(0 - 0)² + (2 - 0)²] = √4 = 2

So, the equation of the circle is:

x² + y² = 2²

Substituting (1, √3) into the equation of the circle, we get:

1² + (√3)² = 2²

1 + 3 = 4

4 = 4

Since the equation is true, point (1, √3) lies on the circle centered at the origin and contains the point (0, 2).

Therefore, we have proven that point (1, √3) satisfies the equation of the circle and lies on the circle.

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To achieve an equal mixture of milk and water, we need to remove and replace some of the mixture with water. Let's assume that we start with a certain amount of the mixture, and we remove x% of it and replace it with an equal amount of water.

To determine the value of x, we can use the following approach:

First, let's assume that we start with 100 units of the mixture. Therefore, we have 75 units of milk and 25 units of water in the mixture.

If we remove x% of the mixture, we will have (100 - x)% of the original amount left. After removing x%, the amount of milk in the mixture will still be 75 units, but the amount of water will be (75/25)*x = 3x units.

Now, we replace the removed x% of the mixture with an equal amount of water. Therefore, the amount of water in the mixture will increase by x% of the original amount, which is 25x/100. After the replacement, the amount of milk in the mixture will still be 75 units, but the amount of water will be (25 + 25x/100) units.

To achieve an equal mixture of milk and water, we need the amount of milk to be equal to the amount of water. Therefore, we can set up the following equation:

75 = (25 + 25x/100)/(2)

Solving for x, we get x = 33.33%.

Therefore, we need to remove and replace 33.33% of the mixture with water to achieve an equal mixture of milk and water.

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Answer:

A: discrete data — because number of bottles can only be whole numbers and thus discrete

B: continuous data — time is a continuous variable

C: qualitative data — there are categories of different sports so this is qualitative.

Answer:

m = -3

Step-by-step explanation:

5m + 20 = 8 + 2m +3

5m + 20 = 11 +2m

3m + 20 = 11

3m = -9

m = -3

Answer:

3

Step-by-step explanation:

The value of x, y, and z are -2, -11, and -3 respectively after solving with substitution method option (B) is correct.

It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.

We have given two matrices that represents the solution to the system of equations.

\(= \rm \left[\begin{array}{ccc}4&-1&0\\0&1&4\\3&0&-2\end{array}\right] \left[\begin{array}{ccc}3\\-23\\0\end{array}\right]\)

The equations are:

4x - y = 3  ...(1)

y + 4z = -23  ...(2)

3x - 2z = 0  ...(3)

After solving with the substitution method we get:

x = -2

y = -11

z = -3

Thus, the value of x, y, and z are -2, -11, and -3 respectively after solving with substitution method option (B) is correct.

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