Find the values of x and y

Answer:

$5

Step-by-step explanation:

Number of hours worked = 32

Total pay = $160

So, hourly rate

= Total pay/number of hours worked

= $160/32

= $5

Answer:

Step-by-step explanation:

The bell boy added $270 and $20 incorrectly. The $20 bill was something that was returned due to overcharching. On the other hand, $270 was the amount that they paid for their room. This only means that $20 should be deducted from $270 and that's the amount that they paid for their room while $30 and $20 are the amount that the bell boy received as a tip

Total money of the three men: 3($100) = $300

They paid $270 for the room: $300 - $270 = $30

Tip for the bell boy: $30 - $30 = $0

Amount overcharged to them: $0 + $20 = $20

Tip to the bell boy: $20 - $20 = $0

They were left with no more money from the original $300.

Answer:

0.41, 43.5%, 9/2.

Answer:

1/9 rise 1 run 9

Step-by-step explanation:

if you graph the y coordinate as 3 and find the x value, x value should be 0. Point (0,3) and (-9,2) and do rise over run

Answer:

Parallel: -1/2

Perpendicular: 2

Step-by-step explanation:

The slope of a line parallel to another, always has the same slope as the line that it is parallel to.

The slope of a line perpendicular to another, always has the opposite reciprical to the line that it is perpendicular to.

Answer:

The original price of the shirt was Ksh 500 and it was sold for Ksh 550.

The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.

To find the percentage discount, we can use the formula:

percentage discount = (discount ÷ original price) × 100%

percentage discount = (-50 ÷ 500) × 100%

percentage discount = -10%

Therefore, the percentage discount is 10%.

Answer: Sam was 2.5 Km far from his house

Step-by-step explanation:

Sam's parents gave him a map to reach his house.

As per Map Sam was =1.5cm from his home.

To find actual distance from house

If we consider actual distance  of sam house =X

We have,

If each 3 cm on scale drawing equals 5 km

We know on map 3cm  = 5Km

If 1.5 cm = X Km

We need to cross multiple

 3X =1.5 × 5

 3X = 7.5

X= 7.5÷3

X= 2.5 Km

Sam was 2.5 Km far from his house.

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Answer:

24663.9!

Step-by-step explanation:

The required cost of the loan is given as $100,966.80.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
Bought a new house for $195,000.
Financed the house and the monthly payments are $822.13 a month for 30 years.

Total money paid against the loan = 822.13 × 30 × 12
                                                    = $295,966.8

Cost of the loan = 295,966.8 - 195,000
                         = $100,966.8

Thus, the required cost of the loan is given as $100,966.80.

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In a nutshell, steps 1, 2, 3 and 4 are correct. (Correct choices: II, III, IV, V)

Herein we have the trascendent equation tan 39° = 12 / x, in which x can be cleared within the expression solely by algebraic approach. The complete procedure is shown below:

tan 39° = 12 / x                  Given

tan 39° = 12 · x⁻¹                Definition of division / Existence of the multiplicative inverse

x · tan 39° = 12                  Compatibility with multiplication / Associative, commutative and modulative properties / Existence of the multiplicative inverse      (Steps 1 & 2)

x = 12 · (tan 39°)⁻¹              Compatibility with multiplication / Associative, commutative and modulative properties / Existence of the multiplicative inverse    

x = 12 / tan 39°                  Definition of division / Result         (Steps 3 & 4)

In a nutshell, steps 1, 2, 3 and 4 are correct. (Correct choices: II, III, IV, V)

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The solution for the given system of equations is

x = 3

y = -12

What are linear equations in two variables?

Therefore, a linear equation in two variables is any equation that can be written in the form ax + by + c = 0, where a, b, and c are real values, and a and b are not equal to zero.

Given two linear equations of two variables.

y = -4x .....eq 1

6x - y = 30 .....eq 2

We have to solve them using substitution.

Now,

by substituting eq 1 in eq 2,

6x -(-4x) = 30

6x + 4x = 30

10x = 30

x = 3

from eq 1,

y = -4x = -4*3 = -12

Therefore, x = 3 and y = -12

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Answer:

she would walk at least those 62 miles

Step-by-step explanation:

We are told that in the 3 days of the walk to fight cancer, Mary breaks the 62 mile barrier every day, that is to say that every day she travels 62 miles or more.

You ask us how much she walks in a single day, considering what the statement that goes at least 62 miles each day says, she would walk at least those 62 miles on a normal day.

Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

Answer:

b. The speed of the car is an explanatory variable

Step-by-step explanation:

In the scenario above, the variable which the researcher intends to measure is the a distance covered by a car using the speed information available. The measured variable is the dependent variable as it outcome depends on the variable with which it is being measured, this is called the independent or explanatory variable.

Therefore, car speed is the explanatory or independent variable

Distance is the dependent, response or measured variable.

Answer:

We first find the volume of water without the stone.

V1 = 10 *(π * 52) = 250 π , where π = 3.14

The volume of water and stone is given by

V2 = 13.2 *(π * 52) = 330 π

The volume of the stone is given by

V2 - v1 = 330 π - 250 π = 80 π

= 251.1 cm3

Answer: 400

Step-by-step explanation:

Answer: 147.2

Step-by-step explanation:

(8+15) = 23

23 x 6.4= 147.2

Answer: 147.2

Step-by-step explanation: 8+15= 23 so 23*6.4 is 147.2

Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

Answer:

59

9/5(15)+32 =59

Step-by-step explanation:

If f(x,y,z) = x²+y²+z² and W is the solid cylinder with height 5 and base radius 2 that is centered about z-axis with its base at z=-1 then the integral value is 432π.

They want f inside the integral so your integer and is: (x² + y² + z²) rdzdrdt

Note that you need another r because you are integrating in cylindrical

coordinates.

conversion equations:

x = rcost

y = rsint

x² + y² = r²

(x² + y² + z²)rdzdrdt becomes (r² + z²)rdzdrdt

W is the solid cylinder with height of 3, radius of 4, and centered about the z-axis, starting from z = -1.

Around the z-axis, cylinders take the forms of circles: x² + y² = r²

This cylinder will have the equation: x² + y² = 16

Its height is 3 so from z = -1 to z = 2

z bounds: -1 <= z <= 2

r bounds (based on the circle): 0 <= r <= 4

t bounds (based on the circle): 0 <= t <= 2pi

\(\int_{0}^{2\pi}\int_{0}^{4}\int_{-1}^{2}(r^{2}+z^{2})rdzdrdt\)

(r² + z²)r = r³ + rz²
dz integral gives: r^3*z + (1/3)rz^3 --> 2r^3 + (8/3)r - (-r^3 - (1/3)r)

= 2r^3 + (8/3)r + r^3 + (1/3)r

= 3r^3 + 3r

dr integral gives: (3/4)r^4 + (3/2)r^2 --> 216

dt integral gives: 216t --> 432pi

Hence we get the integral value as 432π

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The p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis. There is insufficient evidence to support the claim p-value greater than the significance level 0.05.

Consider the above given that

⇒\(& \alpha=0.05 \quad \mathrm{n}=34 \mathrm{~s}^2=0.0005 \\\)

⇒\(H_{0} : \sigma^2 \leq 0.0004 \\\)

⇒\(H_{a} : \sigma^2 > 0.0004\)

The null and alternative hypothesis test statistic:

⇒\(& \mathrm{x}^2=\left(\frac{\mathrm{n}-1}{\sigma^2}\right) \mathrm{s}^2 \\\)

\(& =\left(\frac{34-1}{0.0004}\right) 0.0005 \\\)

⇒\(& \mathrm{x}^2=\left(\frac{33}{0.004}\right) \times 0.0005 \\\)

\(& =82,500 \times 0.0005 \\\)

⇒\(& \mathrm{x}^2=41.25\)

⇒\(h_{0} : $\sigma^2$ is that or equal to $0.0004$\)

⇒\(h_{a} : $\sigma^2$ is greater that $0.0004$\)

⇒p value=p(z>41.25)

⇒p value=0.1533

By using P Value from Chi-Square Calculator

⇒p value=0.1533

⇒P value >0.05

Fail to reject the null hypothesis.

Therefore, the p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis.

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The competitive advantage of some small Americans factories such as in tolerance contract manufacturing lies in their ability to produce parts with very narrow requirements, or tolerances, that are typical in the aerospace industry. consider a product with specifications that call for a maximum variance in the lengths of the parts of 0.0004. suppose the sample variance for 34 parts turns out to be \(s^{2}=0.0005\) . use \(\alpha=0.05\) , to test whether population variance specification is violated.

\(H_{0} \\H_{a}\)

Test statistic:

The p-value is-------.

Answer:

The total weight of the file was 64 mb.

Step-by-step explanation:

Given that Rachel downloaded a movie at a constant speed, and after she downloaded 40% of the movie, the remaining download time was 40 seconds, while after she downloaded 40 mb, the remaining download time was 16 seconds, to determine the total size of the movie rounded to the nearest mb, the following calculation must be performed:

100 - 40 = 60

60% = 40 seconds

40 mb = 16 seconds left

16/40 = 4/10

60/40 = 1.5

1.5% for every 1 second of download.

16 x 1.5 = 24

40 + 24 = 64

Thus, the total weight of the file was 64 mb.

Answer:

4(9x-7)

Step-by-step explanation:

Answer:

4(9x-7)

Step-by-step explanation:

Answer:

y = -13/10x + 2/5

Hope this helps!

The parabola \(y = √(x - 4)\) opens upward.

The parabola y = √(x - 4) represents the square root function of x minus 4. To determine the direction in which the parabola opens, we examine the behavior of the square root function.

The square root function (√x) returns non-negative values for non-negative inputs. Since the expression inside the square root, (x - 4), must be non-negative for real solutions, we have x - 4 ≥ 0. Solving this inequality, we find x ≥ 4.

This means that the parabola is defined for x values greater than or equal to 4. As we increase x from 4, the value of √(x - 4) will also increase. Therefore, the graph of the parabola opens upward.

The parabola \(y = √(x - 4)\) opens upward.

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Answer:

The answer is 22

Step-by-step explanation:

might be wrong so I would wait for someone else to also answer.

Answer:

How many classes is Gina taking?

Answer:

10

Step-by-step explanation:

right on edge

By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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Answer:

7.4

Step-by-step explanation:

When the decimal in any place is more than 0.5, round up.