Substitute and simplify.
w = -6, x = 4, y = 3, z = -8
1. WX + YZ =
2. 2w + 3z- xy + z³ =
3. y(z + x) =
4. (W+x+y)³=
5. (z-w)³ =
6. 5(w + x) + 4(y + z) =
7. W² - x² =
8. (xy) – 2wz =
9. wz - 4xy =
10. w+ (x+y+z)² =

The Original Price of helmet is $20.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The helmet Clare plans to buy is on sale for 20% less than the original price.

let the sale price be x.

So, the Original price is (x+5).

Also, Sales price = Original price - 20% of Original price

x= x+ 5 - 0.20(x+5)

x = x+ 5 - 0.20x - 1

0.20x = 4

x= 4/ 0.20

x= $20

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Answer:

0.609

Step-by-step explanation:

convert to a fraction then convert to a decimal by dividing the numerator and denominator :)

Answer: To find out how much you would pay for 2.5 kg of tomatoes at $1.50 per kg, we need to multiply the weight of the tomatoes by the price per kg:

Cost = 2.5 kg x $1.50/kg

   = $3.75/kg x 2.5 kg

   = $9.38

So, you would pay $9.38 for 2.5 kg of tomatoes at $1.50 per kg.

Step-by-step explanation:

The amount of time it require to water all the parts of her lawn is, 63 minutes

Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.

We denote division by '÷' this symbol.

Given that,

Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn.

Each station runs for an equal amount of time

it takes 49 minutes for the first 7 stations to water

The amount of time it require to water stations = ?

First, we need to calculate time required to water 1 station,

t =  Total time taken / Total station watered

  =   49 / 7

  =   7  minutes/station

So

Time for water all parts = 7 x 9

                                       = 63 minutes

Hence, the required time is 63 minutes

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Answer: 5x^-10 * -2x^4

To simplify this expression, we will multiply the coefficients (the numbers in front of the variables) and add the exponents of x.

5 * -2 = -10

-10x^(-10 + 4) = -10x^-6

So, the simplified expression is:

-10x^-6

2.-4x^2 * 3y^-5 * 2y^7 * x^-6

To simplify this expression, we will multiply the coefficients and add the exponents of x and y.

-4 * 3 * 2 = -24

-24x^2 * y^(-5 + 7) * x^(-6)

-24x^2 * y^2 * x^-6

-24x^(2 - 6) * y^2

-24x^-4 * y^2

So, the simplified expression is:

-24x^-4 * y^2

Step-by-step explanation:

(a). Name of internet service provider is categorical variable because it cannot be quantified or measured. It can be divided into different categories according to the service they provide.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

(b). Time in hours, spent surfing the internet per week is continuous numerical variable because time can be measured over an infinite number of real values within a given interval.

A variable is said to be continuous if it can assume an infinite number of real values within a given interval.

Measurement scale used for determination is ratio scale.

(c). Whether the individual uses a mobile phone to connect to the internet is categorical variable because the answer can only be yes or no and it cannot be measured numerically.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

(d). Number of online purchases made in a month is discrete numerical variable because it is a value that arises through a counting process.

A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation.

Measurement scale used for determination is interval scale.

(e). Where the individual uses social networks to find sought -after information is categorical variable because the answer can only be yes or no and it cannot be measured numerically. It can be either he/she uses or he/she do not.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

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Each cone has a volume of around 60 [tex]cm^{3}[/tex]. As a result, 800 [tex]cm^{3}[/tex] of cream would be sufficient to fill around 13 cones.

The quantity of space that an item or substance occupies is measured by its volume. Typically, it is expressed in cubic quantities like cubic metres or cubic feet. Volume is frequently used to describe liquids, gases, or other pourable materials like a cup of water or a gallon of fuel. The capacity of a container, such as a tank or box, is also determined by volume.

In this question, the volume of a cone is given by the formula:

V = (1/3)π[tex]r^{2} h[/tex]

Where r is the radius of the base and h is the slant height.

In this case, the radius of the base is equal to half the base diameter (4.2/2 = 2.1 cm) and the slant height is 7.5 cm.

So, the volume of each cone is (1/3)π x (2.1)2 x 7.5 = 28.7 cm3

Therefore, the number of cones needed to fill the ice cream cone with 800 cm3 of cream is 800/28.7 = 27.9 (rounded up to 28).

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The y-intercept of the graph of a function is the point at which the graph intersects the y-axis. In other words, it's the value of the function when x=0.

So to find the y-intercept of f(x) = 57(3.2)x, we can substitute x=0 into the function:

f(0) = 57(3.2)(0)

f(0) = 0

So the y-intercept of this function is (0,0).

Answer:

$51

Step-by-step explanation:

At each age his grandmother gives him three times his age in money.

3 x 5

3 x 8 ...

Answer: Solutions for x - 4,4,-5 and for y - 3,-3, 0

Step-by-step explanation: I wrote the solutions in order. To solve this question I combined both equations to eliminate the y variable to solve for x. It looked like this :  [tex]x^2+x=20[/tex]. I brought the 20 to the other side and got [tex]x^2+x-20=0[/tex]. Then I factored and got [tex](x+5)(x-4)[/tex] which means x = -5 and x = 4. Finally I plugged in these values into the equation to find the possible y values.

A hypothesis that there is some sort of relationship between the variables is where scientists start their inquiry. The alternative, or null hypothesis, asserts that there is no such relationship. Although the null hypothesis may not appear fascinating, it is a crucial component of research.

The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis. A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.

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The correct equations for the measures of the unknown angles x and y are:

x = cos(a), y = sin(a).

The trigonometric functions (sin, cos, tan) are mathematical functions that describe the relationships between the sides and angles of a right triangle. Given an angle a in a right triangle, we can use these functions to find the values of the side ratios for that angle. For example:

sin(a) = opposite side / hypotenuse

cos(a) = adjacent side / hypotenuse

tan(a) = opposite side / adjacent side

In these expressions, "opposite side" refers to the side opposite the angle a, "adjacent side" refers to the side adjacent to the angle a, and "hypotenuse" refers to the longest side in the right triangle (the one opposite the right angle).

The inverse trigonometric functions[tex](sin^-1, cos^-1, tan^-1)[/tex] are the reverse of the trigonometric functions. Given a value of a trigonometric function, the inverse function returns the measure of the angle (in radians) for which that value is the result. For example:

[tex]sin^-1(y) = a (where y = sin(a))cos^-1(x) = a (where x = cos(a))tan^-1(t) = a (where t = tan(a))[/tex]

So, the correct equations for the measures of the unknown angles x and y are:

[tex]x = cos^-1(x)y = sin^-1(y)[/tex]

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Answer: 3.6

Step-by-step explanation:

3/5 is equal to 20% (3 divided by 5 times 100)

1.2 is 20% of 6

So, 3.6 is 3/5 of 6

Lauren was 13 miles away from the restaurant when Aidan reached it.

Travel refers to the act of moving from one place to another, often over a distance or by means of transportation.

Lauren and Aidan both left their offices at 6:15 P.M. and traveled for 20 minutes (from 6:15 P.M. to 6:35 P.M.) before Aidan arrived at the restaurant. During this time, Lauren traveled at a speed of 39 miles per hour, so she covered a distance of:

distance = speed x time

distance = 39 miles/hour x (20 minutes / 60 minutes/hour) = 13 miles

After 20 minutes, Aidan arrived at the restaurant, having traveled for 20 minutes at a speed of 42 miles per hour. The distance he covered during this time is:

distance = speed x time

distance = 42 miles/hour x (20 minutes / 60 minutes/hour) = 14 miles

Since they both traveled the same distance to the restaurant, but Aidan arrived there first, Lauren must have been 1 mile behind him when he arrived at the restaurant.

Therefore, Lauren was 14 - 1 = 13 miles away from the restaurant when Aidan reached it.

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Answer:

I think it’s 730 days

Step-by-step explanation:

Answer:

The first/top option

Step-by-step explanation:

First, we can find the inequality that the line is representing. X is the number of hours she has already done, and she has five hours more to do to fulfill the 12 or more hours of required service. The inequality would be x+5≥12.

The minimum that X has to be is 7 because any value lower than 7 would make the inequality false[ ex. 6 + 5 ≠ 12 ]. The arrow would be pointing to the right, because 7 is the minimum value, not the max, so any value higher than 7 would still make the inequality true. Lastly, the circle would be filled, because 7 is included in the set of values that make the inequality true[ 7 + 5 = 12 ].

So, the answer would be the first option.

Answer:

f(-2) = 2

Step-by-step explanation:

Using the graph, we can determine the y value when x = -2.

When x = -2, the y value is 2.

f(-2) = 2

Answer:122 cars per hour

Step-by-step explanation:Get the total number of cars 610 get the time period 5 hours divide 610 divided by 5 equals 122 cars per hour.

Answer: the ferry took atleast 3,050 cars each hour

Answer:

x = 2.0909090

Step-by-step explanation:

Here is my solution.

The equation x-3/ 2y=-12 when solved for the variable y is y = x-3/-24

We have to make 'y' the subject from the equation, we have;

x-3/2y=-12

By solving for the variable, we need to work it out.

Also, we have to make it stand alone on one end of the equality sign.

cross multiply the values

x - 3(1) = -12(2y)

multiply the values

x-3 = -24y

Make 'y' the subject by dividing both sides by the coefficient of y

y = x-3/-24

Hence, the equation is y = x-3/-24

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Probability that a randomly chosen part (a) has a P(flaw) = 0.2 and

has no major flaws b) P(No major flaws) = 0.95

The probability that an event will occur is determined by probability: P(A) = f / N. Probability and odds are related, but probability determines what the odds are. Probability is required before calculating the likelihood that an event will occur.

To find the probability of flaws, we can find the probability of no flaws first by dividing by 100:

P(no flaw) = 80/100 = 0.8

So then:

P(flaw) = 1 - P(no flaw) = 1 - 0.8 = 0.2

P(flaw) = 0.2

B) First, we need to find the probability of major flaws:

P(major flaws) =

P(Major flaws) = 0.05

So to find the probability of no major flaws:

P(No major flaws) = 1 - P(major flaws) = 1 - 0.05 = 0.95

P(No major flaws) = 0.95

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The required value of x for the diagonals of parallelogram is 8.

Let ABCD be the parallelogram, and let the diagonals AC and BD intersect at point E.

We know that in a parallelogram, the diagonals bisect each other. So, we have:

AC = 2AE and BD = 2BE

We are given that AC = 4x + 2 and BD = 5x - 6. Substituting in the above equations, we get:

2AE = 4x + 2 and 2BE = 5x - 6

Dividing both sides by 2, we get:

AE = 2x + 1 and BE = (5x - 6)/2

Since AE and BE are the same length (they are both half the length of the diagonals), we have:

2x + 1 = (5x - 6)/2

Multiplying both sides by 2, we get:

4x + 2 = 5x - 6

Subtracting 4x from both sides, we get:

8 = x

Therefore, the value of x is 8.

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Answer: 90 miles in 180 minutes

Step-by-step explanation: Since 90 minutes is two times 45, there would be 2 miles in one minute. Then, you multiply 2 times 45 so therefore you get 90 miles in 180 minutes.

The sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl. The test statistic is 50 and then the p-value is 32.93

Mean is the ratio of the sum of all observations to the number of observations. Standard deviation is the measure in which it shows how much the variation such as spread, dispersion,  from the mean exists and the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.

For the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.

Given that, exercise n =64

mean  = 11.3 mg/dl

standard deviation = 1.6mg/dl

The test statistic is 50

the p-value is calculated by, (n-mean) / (standard deviation)

(64 - 11.3) / (1.6)

32.93

Therefore, the p-value in which it obtains a more precise value is 32.93

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Answer:

CD = 36°

Step-by-step explanation:

the measure of secant angle BFE is half the difference of the measures of the intercepted arcs , that is

[tex]\frac{1}{2}[/tex] (BE - CD) = ∠ BFE

[tex]\frac{1}{2}[/tex] (128 - x) = 46 ( multiply both sides by 2 to clear the fraction )

128 - x = 92 ( subtract 128 from both sides )

- x = - 36 ( multiply both sides by - 1 )

x = CD = 36°

Answer:

A = 648π cm²

Step-by-step explanation:

the area (A) of a semicircle is half the area of a circle , then

A = [tex]\frac{1}{2}[/tex] πr² ( r is the radius ) , then

A = [tex]\frac{1}{2}[/tex] × π × 36² = [tex]\frac{1}{2}[/tex] × π × 1296 = 648π cm²

The dilated points are:

W': (-1, 2)

X': (2.5, 0)

Y': (-0.5, -2).

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.

Given:

Triangle WXY with vertices W(-4, 8), X (10, 0), and Y(-2, -8).

And the scale factor is 1/4.

So, the image points are,

W': (-4/4, 8/4) = (-1, 2)

X': (10/4, 0/4)  = (2.5, 0)

Y': (-2/4, -8/4) = (-0.5, -2)

Hence, the image points are given above.

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The solution is Option A.

The conversion factor should have gallons in the denominator and the equation will be 350 gallons = 92.3 L

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the amount of gallons of water be = 350 gallons

And , 1 gallon = 3.79 liters

So , the amount of 350 gallons = ( 350 ) x ( 1/3.79 ) L

Substituting the values in the equation , we get

The amount of 350 gallons = ( 350 / 3.79 ) L

On simplifying the equation , we get

The amount of 350 gallons = 92.3 L

Therefore , while converting the gallons to liters , the factor of gallons should be in the denominator

Hence , the equation is 350 gallons = 92.3 L

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Based on the traffic flow model, the city should close the road with the least amount of traffic. From the diagram, we see that the road with the least amount of traffic is Salisbury St.

(a) Constraints:

The flow into and out of Jones St. is equal to the total flow into and out of Salisbury St. and Edenton St.

The flow into and out of McDowell St. is equal to the total flow into and out of Salisbury St. and Edenton St.

The flow into and out of Salisbury St. is equal to the sum of the flow into and out of Jones St. and McDowell St.

The total flow into and out of each street must be greater than or equal to 0.

Let x, y, z, and w be the traffic flow in cars per hour along Jones St., Salisbury St., Edenton St., and McDowell St., respectively. Then the system of linear equations that models this scenario is:

x - y - z = 0

w - y - z = 0

y + z - x - w = 0

x, y, z, w ≥ 0

(b) Augmented matrix representation:

[1 -1 -1 0 | 0]

[0 -1 -1 1 | 0]

[1 -1 1 -1 | 0]

[1 0 0 0 | 0]

Gauss-Jordan reduction:

[1 0 0 0 | 0]

[0 1 0 0 | 0]

[0 0 1 0 | 0]

[0 0 0 0 | 0]

The final augmented matrix is shown above. The solution to the system is x = 0, y = 0, z = 0, and w = 0.

(c) If the city were to close one of these 4 roads, then the traffic would have to be rerouted. Based on the traffic flow model, the city should close the road with the least amount of traffic. From the diagram, we see that the road with the least amount of traffic is Salisbury St. Therefore, the city should close Salisbury St.

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Step-by-step explanation:

[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]

So let find cos

We know that

[tex] \tan {}^{2} (x) + 1 = \sec {}^{2} (x) [/tex]

We know the value of tan

[tex]( \frac{8}{5} ) {}^{2} + 1 = \sec {}^{2} (x) [/tex]

[tex] \frac{64}{25} + 1 = \sec {}^{2} (x) [/tex]

[tex] \frac{89}{25} = \sec {}^{2} (x) [/tex]

[tex] \frac{ \sqrt{89} }{5} = \sec(x) [/tex]

Sec is the reciprocal of cosine so cosine is

[tex] \cos( \alpha ) = \frac{5}{ \sqrt{89} } [/tex]

Which becomes

[tex] \cos( \alpha ) = \frac{5 \sqrt{89} }{89} [/tex]

So since we know cos a, let's find sin

[tex] \sqrt{ \frac{1 - \frac{5 \sqrt{89} }{89} }{2} } [/tex]

[tex] \sqrt{ \frac{89 - 5 \sqrt{89} }{2} } [/tex]