Which system of equations shows a solution of (0.5, -1)?
Need answers asap plzzz

Answer:

1.125 hours

Step-by-step explanation:

Given :

Ben's speed = 3 mi/hr

Time before Amanda starts = 1.5 hours

Amanda's speed = 7 mi/hr

Time before Amanda catches up with Ben

Recall :

Distance = speed * time

Distance already covered by Ben before Amanda starts :

(3 * 1.5) = 4.5

Hence, we can setup the equation :

Ben's distance = Amanda's distance

Let time taken = x

4.5 + 3x = 7x

4.5 = 7x - 3x

4.5 = 4x

x = 4.5 / 4

x = 1.125 hours

1.125 * 60 = 67. 5 minutes

Answer:

(1.218 ; 1.322)

the confidence interval is appropriate

Step-by-step explanation:

The confidence interval :

Mean ± margin of error

Sample mean = 1.27

Sample standard deviation, s = 0.80

Sample size, n = 914

Since we are using tbe sample standard deviation, we use the T table ;

Margin of Error = Tcritical * s/√n

Tcritical at 95% ; df = 914 - 1 = 913

Tcritical(0.05, 913) = 1.96

Margin of Error = 1.96 * 0.80/√914 = 0.05186

Mean ± margin of error

1.27 ± 0.05186

Lower boundary = 1.27 - 0.05186 = 1.218

Upper boundary = 1.27 + 0.05186 = 1.322

(1.218 ; 1.322)

According to the central limit theorem, sample means will approach a normal distribution as the sample size increases. Hence, the confidence interval is valid, the sample size of 914 gave a critical value at 0.05 which is only marginally different from that will obtained using a normal distribution table. Hence, the confidence interval is appropriate

Answer:

hope it is helpful to you

The simplified form of statement 155 plus 33 minus 4 divided by 2 is

186.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

The given statement is 155 plus 33 minus 4 divided by 2 which can be numerically expressed as,

155 + 33 - 4 ÷ 2.

PEMDAS rule states the correct order of simplifying an expression is as follows, Parenthesis, exponents, multiplications, divisions, additions, and, subtractions.

155 + 33 - 2.

= 188 - 2.

= 186.

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Answer:

use blue red blue red

Step-by-step explanation:

Answer:

H0 : ρ = 0

H1 : ρ ≠ 0

Test statistic = 1.197

Pvalue = 0.2335

There is no correlation between the two variables

Step-by-step explanation:

The null and alternative hypothesis :

H0 : No correlation exist,

H1 : Correlation exist

H0 : ρ = 0

H1 : ρ ≠ 0

Test statistic, T = r / √(1 - r²) / (n - 2)

T = 0.067 / √(1 - 0.067²) / (320 - 2)

T = 0.067 / √(0.995511 / 318)

T = 0.067 / 0.0559512

T = 1.197

The Pvalue obtained from the Rscore, at df = 320 - 2 = 318 is 0.2335

α = 5% = 0.05

The Pvalue > α ; we fail to reject the null and conclude that, there is no correlation between the two variables.

Answer:

57 cm²

Step-by-step explanation:

Surface area of the yellow prism = front + back + right + left + top

✔️Area of the front = L * W

L = 4 cm

W = 3 cm

Area of the front = 4*3 = 12 cm²

✔️Area of the back = L * W

L = 4 cm

W = 3 cm

Area of the back = 4*3 = 12 cm²

✔️Area of the right face = L * W

L = 4 cm

W = 3 cm

Area of the right face = 4*3 = 12 cm²

✔️Area of the left face = L * W

L = 4 cm

W = 3 cm

Area of the left face = 4*3 = 12 cm²

✔️Area of the top = L * W

L = 3 cm

W = 3 cm

Area of the top = 3*3 = 9 cm²

✅Total = 12 + 12 + 12 + 12 + 9 = 57 cm²

Answer:

[tex]P(Positive\ Mixture) = 0.2775[/tex]

The probability is not low

Step-by-step explanation:

Given

[tex]P(Single\ Positive) = 0.15[/tex]

[tex]n = 2[/tex]

Required

[tex]P(Positive\ Mixture)[/tex]

First, we calculate the probability of single negative using the complement rule

[tex]P(Single\ Negative) = 1 - P(Single\ Positive)[/tex]

[tex]P(Single\ Negative) = 1 - 0.15[/tex]

[tex]P(Single\ Negative) = 0.85[/tex]

[tex]P(Positive\ Mixture)[/tex] is calculated using:

[tex]P(Positive\ Mixture) = 1 - P(All\ Negative)[/tex] ---- i.e. complement rule

So, we have:

[tex]P(Positive\ Mixture) = 1 - 0.85^2[/tex]

[tex]P(Positive\ Mixture) = 1 - 0.7225[/tex]

[tex]P(Positive\ Mixture) = 0.2775[/tex]

Probabilities less than 0.05 are considered low.

So, we can consider that the probability is not low because 0.2775 > 0.05

Answer:

C

Step-by-step explanation:

For this, you want to treat i like any other variable, and combine like terms. However you need to keep in mind that there is a negative sign before the second set of parentheses. This means everything inside it should have a negative before it. So we can write it like this:

(7 + 3i) - (3 - 9i)

7 + 3i -3 +9i

4 + 12i

Hope that helps!

Answer:

y = 4x + 26

Step-by-step explanation:

y = mx + b

The slope (m) is equal to 4.

y = 4x + b

To find the y-intercept (b), plug in the point given.

6 = 4(-5) + b

6 = -20 + b

26 = b

The answer is y = 4x + 26.

Answer:

The equation of the line passing through (-5, 6) with a slope of 4 is

y = 4x + 26

Step-by-step explanation:

An equation of a line would always have the following structure...

y = mx + b

In this equation, "y" is the y coordinate of the point, "x" is the x coordinate of the point, "m" is the slope, and "b" is the y coordinate of the y-intercept. We know all the values except "b", but we can find the value of "b" by substituting all the other values into the equation...

y = mx + b

6 = 4(-5) + b

6 = b - 20

b = 6 + 20

b = 26

Therefore, the equation of the line passing through (-5, 6) with a slope of 4 is y = 4x + 26

Answer:

Part A)

2048π/3 cubic units.

Part B)

8192π/15 units.

Step-by-step explanation:

We are given that R is the finite region bounded by the graphs of functions:

[tex]f(x)=4\sqrt{x}\text{ and } g(x)=x[/tex]

Part A)

We want to find the volume of the solid of revolution obtained when rotating R about the x-axis.

We can use the washer method, given by:

[tex]\displaystyle \pi\int_a^b[R(x)]^2-[r(x)]^2\, dx[/tex]

Where R is the outer radius and r is the inner radius.

Find the points of intersection of the two graphs:

[tex]\displaystyle \begin{aligned} 4\sqrt{x} & = x \\ 16x&= x^2 \\ x^2-16x&= 0 \\ x(x-16) & = 0 \\ x&=0 \text{ and } x=16\end{aligned}[/tex]

Hence, our limits of integration is from x = 0 to x = 16.

Since 4√x ≥ x for all values of x between [0, 16], the outer radius R is f(x) and the inner radius r is g(x). Substitute:

[tex]\displaystyle V=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} \displaystyle V&=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx \\\\ &=\pi\int_0^{16} 16x-x^2\, dx \\\\ &=\pi\left(8x^2-\frac{1}{3}x^3\Big|_{0}^{16}\right)\\\\ &=\frac{2048\pi}{3}\text{ units}^3 \end{aligned}[/tex]

The volume is 2048π/3 cubic units.

Part B)

We want to find the volume of the solid of revolution obtained when rotating R about the y-axis.

First, rewrite each function in terms of y:

[tex]\displaystyle f(y) = \frac{y^2}{16}\text{ and } g(y) = y[/tex]

Solving for the intersection yields y = 0 and y = 16. So, our limits of integration are from y = 0 to y = 16.

The washer method for revolving about the y-axis is given by:

[tex]\displaystyle V=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy[/tex]

Since g(y) ≥ f(y) for all y in the interval [0, 16], our outer radius R is g(y) and our inner radius r is f(y). Substitute and evaluate:

[tex]\displaystyle \begin{aligned} \displaystyle V&=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy \\\\ &=\pi\int_{0}^{16} (y)^2- \left(\frac{y^2}{16}\right)^2\, dy\\\\ &=\pi\int_0^{16} y^2 - \frac{y^4}{256} \, dy \\\\ &=\pi\left(\frac{1}{3}y^3-\frac{1}{1280}y^5\Bigg|_{0}^{16}\right)\\\\ &=\frac{8192\pi}{15}\text{ units}^3\end{aligned}[/tex]

The volume is 8192π/15 cubic units.

Answer:

387287i32

Step-by-step explanation:

i did it

Answer:

5 sandwiches he made in bread

The answer is (a)..........

Answer:

A) Hence, the number of coffee cups that are risky = 17.4 Cups.

B) Here, the number of coffee cups that are risky = 59.5 Colas.

Step-by-step explanation:

A)

In 1 cup coffee  =[tex]8\times21.5mg= 172.0 mg[/tex]

Hence one cup of coffee contains 172 mg of caffeine. The risky level is 3000mg.

Therefore, the number of coffee cups that are risky

                                                         [tex]= 3000/172\\ \\=17.4 cups[/tex]

Here, the number of coffee cups that are risky = 17.4 cups.

B)

[tex]1 cola=12\times4.2mg\\\\ = 50.4mg / day[/tex]

Hence, one can cola contains 50.4 mg of caffeine.

The dangerous level is 3000 mg.

Therefore, the number of cola cans that are risky [tex]=3000/50.4= 59.5[/tex] cola is risky.

Answer:

Step-by-step explanation:

they say by noon 4 inches of rain has fallen,    then the say that it's falling at  1/4 inch per hour

f(x) = 1/4x +4

where x is in hours, and  f(x)  represents the linear graph of the amount of rain that has fallen after noon   :)

so by 2:30   or  2.5 hours....  then

f(2.5) = 1/4x +4

y = 1/4 (2.5) +4  ( i moved to the y  b/c now there is an answer)

y =[tex]\frac{5}{8}[/tex] + 4

y =4[tex]\frac{5}{8}[/tex]   inches of rain

Answer:

a) y = 1/4x + 4

b) 4.625 inches

Step-by-step explanation:

a) y(0) = 4 inches

slope = 1/4 rate

y = 1/4x + 4

b) 12:00pm (noon) to 2:30pm = 2 hours 30 mins = 2.5 hours

y = 1/4x + 4

y = (1/4)(2.5) + 4

y = 0.625 + 4

y = 4.625 inches

Answer:

The domain is "all real numbers" and the range is x more than -3

Answer:

$35,000

Step-by-step explanation:

if $50,000 is to install an area of 1,000 square feet swimming pool and $35,000 can be used to install an 800 square foot swimming pool I think the best graph model is 800 square feet for $35,000 for a cost cut of $15,000 is a good bargain

Answer:

0.0337 = 3.37% probability of finding two defects.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

What is the probability of finding two defects in a Binomial distribution, with a sample size of 30, and probability of 0.2?

This is [tex]P(X = 2)[/tex], with [tex]n = 30[/tex] and [tex]p = 0.2[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 30) = C_{30,2}.(0.2)^{2}.(0.8)^{28} = 0.0337[/tex]

0.0337 = 3.37% probability of finding two defects.

Answer:

[tex]y=\frac{1}{2}x+5[/tex]

Step-by-step explanation:

Hi there!

Slope intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that lie on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug the given points (-4,3) and (6,8) into the equation

[tex]m=\frac{8-3}{6-(-4)}\\m=\frac{8-3}{6+4}\\m=\frac{5}{10}\\m=\frac{1}{2}[/tex]

Therefore, the slope of the line is [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex] :

[tex]y=\frac{1}{2}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{1}{2}x+b[/tex]

Plug in one of the given points and solve for b

[tex]8=\frac{1}{2}(6)+b\\8=3+b[/tex]

Subtract 3 from both sides to isolate b

[tex]8-3=3+b-3\\5=b[/tex]

Therefore, the y-intercept is 5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:

[tex]y=\frac{1}{2}x+5[/tex]

I hope this helps!

Answer:

15=2p+3

Step-by-step explanation:

Answer:

[tex]2 \times \frac{22}{7} \times 10 = 62.87 [/tex]

Answer:

All of these

Step-by-step explanation:

Given

[tex]f(5) = 11[/tex]

[tex]f(x)[/tex] at [tex](5,11)[/tex]

Required

Interpret

[tex]f(5) = 11[/tex] mean that: the function is at [tex](5,11)[/tex]

In other words:

[tex]x = 5; y = 11[/tex]

It also means:

Substitute 5 for x and the result will be 11

Hence, all options are true

Answer:

Graph A

Step-by-step explanation:

correct answer on edge :)

The statement that represents the graphs of the functions f(x) and g(x) : On a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60).

For given question,

The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50 + 10 log x.

If each of the x objects increases its sound power by 10 decibels, then the new total sound power, in decibels, is given by the function

g(x) = f(x) + 10.

The graph of the function f(x) would starts at (0, 50)

For x = 10 the value of the function f(x) would be,

f(10) = 50 + 10 log (10)

f(10) = 50 + 10 (1)

f(10) = 60

This means, the graph of the function f(x) passes though point (10, 60)

Also, the graph of the function g(x) would starts at (0, 60)

For x = 10 the value of the function g(x) would be,

g(10) = f(10) + 10

g(10) = 60 + 10

g(10) = 70

This means, the graph of the function g(x) passes though point (10, 70)

Therefore, on a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60).

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Answer:

[tex]A' = (2,0)[/tex]

Step-by-step explanation:

Given

See attachment for ABCD

[tex]k = \frac{1}{2}[/tex] --- the scale factor

Required

The coordinates of A'

From the attachment, we have:

[tex]A = (4,0)[/tex]

So:

[tex]A' = k * A[/tex]

[tex]A' = \frac{1}{2} * (4,0)[/tex]

[tex]A' = (2,0)[/tex]

Answer:

on khan, both are false

Step-by-step explanation:

Answer:

D. KI

Step-by-step explanation:

KI intersects a minimum of two points meaning it is the definition of a secant.

9514 1404 393

Answer:

  1240 in³

Step-by-step explanation:

The overall dimensions of the block are ...

  10 in by 11 in by 17 in

The volume of that space is ...

  V = LWH = (10 in)(11 in)(17 in) = 1870 in³

The volume of each of the three identical holes is similarly found:

  V = (10 in)(3 in)(7 in) = 210 in³

Then the volume of the block is the overall volume less the volume of the three holes:

  = 1870 in³ - 3(210 in³) = 1240 in³

Answer:

[tex]Pr = 0.153[/tex]

Step-by-step explanation:

Given

[tex]p = 15.3\%[/tex]

Required

Probability of alarm not working

[tex]p = 15.3\%[/tex] implies that the alarm has a probability of not working on a given day.

So, the probability that the alarm will not work on an exam date is:

[tex]Pr = 15.3\%[/tex]

Express as decimal

[tex]Pr = 0.153[/tex]

Answer:

[tex]\sqrt[3]{7x}[/tex]

Step-by-step explanation:

Given

[tex]7x[/tex]

Required

The radical statement

Cube root is represented as:

[tex]\sqrt[3]{}[/tex]

Considering [tex]7x[/tex], the expression is:

[tex]\sqrt[3]{7x}[/tex]