the security system in a house has two units that set off an alarm when motion is detected. neither one is entirely reliable, but one or both always go off when there is motion anywhere in the house. suppose that for motion in a certain location, the probability that detector a goes off and detector b does not go off is 0.25, and the probability that a does not go off is 0.35. what is the probability that b goes off?

The expression when expressed in its exponent is a²+c²

In mathematics, we should understand that exponent tell the power to which a number is raise.

 It shows the number of times a number multiplies itself to get the certain member.

The given expression is a*a*c*.

Using the law of multiplication that says when two or more numbers in the same base are multiplied, we add their powers.

Here a appeared twice a*a=a²

And c appeared twice that is c*c=c²

Combining the two exponents together we have that

a²+c²

In conclusion, the exponent of a*a*a*a is a²+c²

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Answer:

a=82°

b=32°

Step-by-step explanation:

x is the reflection of b

y is the reflection of a

Answer:

30

Step-by-step explanation:

Write the inequality as 150 + 10w > 450.

Then, solve. Draw a line on the inequality symbol, and cross out the 150. Subtract 150 from the other side. Then, divide the 10w by 10, to get w by itself. Since it's inverse operations, divide 450 by 10 as well.

You will get an answer of w > 30.

Thus, Darla needs 30 more subscribers.

Area of a square:

We have s = 6⁴, then the area is:

Or, apply the power of the power rule (xᵃ)ᵇ=xᵃᵇ to get:

By using congruency, it can be calculated that

x = 6, y = 5

What are congruent triangles?

Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same. There are different axioms of congruency. They are-

AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom

It is given that [tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] BAD

So [tex]\angle[/tex]CAB = [tex]\angle[/tex]ABD [Corrosponding parts of congruent triangles are congruent]

4y = 20

y = [tex]\frac{20}{4}\\[/tex]

y = 5

Also,

AC = BD [Corrosponding parts of congruent triangles are congruent]

5x - 3 = 3x + 9

5x - 3x = 9 + 3

2x = 12

x = [tex]\frac{12}{2}[/tex]

x = 6

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Answer:

- When x = 0, f(x) = -5

- Each time x increases by 1, f(x) increase by 3

- f(x) = 3x - 5

Step-by-step explanation:

m = slope of the graph

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x{1}}[/tex]

m  = [tex]\frac{4- (-5)}{3-0}[/tex]

m = [tex]\frac{9}{3}[/tex]

m = 3

[tex]y - y_{1} = m ( x - x_{1})[/tex]

[tex]y - (-5) = 3 ( x - 0 )[/tex]

[tex]y = 3x - 5[/tex]

Answer: S=19cm

Step-by-step explanation:

area = s^2

s(s-5)=266

s^2-5s=266

s^2-5s-266=0

(s-19)(s+14)=0

s=19cm

19 x 19 = 266

The original dimensions of the square cardboard sheet is 19 x 19.

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable, a≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given:

Let the length of each side of the original square cardboard be x cm.

After cutting off a strip of 3cm wide its dimension becomes

length = x cm and breadth= (x−5) cm

So, Area = x² - 5x

266 = x² - 5x

x² - 5x - 266= 0

x² - 19x + 14x - 266= 0

x(x - 19) + 14 (x - 19)= 0

(x- 19)( x + 14) = 0

x= 19, -14.

Hence, the original dimensions of the square cardboard sheet is 19 x 19.

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Answer: no

Step-by-step explanation:

use pythagorean theorem.

you can use a^2+b^2=c^2

the biggest value is always c(the hypotenuse) -> c=20

a and b would be 15 and 17(doesn't matter which is which)

plug it into the equation -> 15^2+17^2=20^2

225+289=400

514≠400

so no, it's not a right triangle

Answer:

2

Step-by-step explanation:

2x - y = -1

-y = -2x - 1

y = 2x + 1

parallel line = same slope

Answer: $28 per week

Step-by-step explanation:

1 month = 4 weeks

18 times 4 = 72 weeks

So you know you want to save 2000 to buy a car 72 weeks from now.

So take 2000 divided by 72 = $27.77 per week

So you need to save about $28 per week.

Answer:

(0,10)

Step-by-step explanation:

You could put any ordered pair, as long as the y value is 10.

The equation of this function is

y = 10  It is a horizontal line going through.  The y intercept is (0,10)                      

Answer: 40 tickets

Step-by-step explanation:

Divide 2,800 by 7

    40

7|  2800|

   28

   0

You get 40. The jazz band would need to sell 40 tickets to meet its goal.

To find the loan amount after five years, we need to calculate the compound interest on the loan. The compound interest is calculated by multiplying the principal (the initial amount borrowed) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 5.75%/12 = 0.475% per month, and there are 12*5 = 60 compounding periods (12 months per year for 5 years).

The compound interest is therefore calculated as follows:

Compound interest = $1,500 * (1 + 0.475%)^60 - $1,500

= $1,725 - $1,500

= $225

So the loan amount after five years is $1,725. Therefore, the correct answer is [D] $1,725.

The equation with value V indicating the decrease in value of iPhone 13 with years t is V = [tex] {1000 (1 - 0.02)}^{t} [/tex].

The equation to be used for the calculation of decreased value is -

A = [tex] {P (1 - r)}^{t} [/tex]. In this formula, A is amount, P is principal, r is rate and t represents time. Based on the information in question, A will be replaced with V. So, the required formula will be -

V = [tex] {P (1 - r)}^{t} [/tex]

Now keeping the values in formula for numerical equation -

V = [tex] {1000 (1 - 0.02)}^{t} [/tex]

Since two values are unknown here, the equation can not be solved further.

Therefore, the required equation is V = [tex] {1000 (1 - 0.02)}^{t} [/tex].

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When they buy 125 identical stuffed animals for $312.50 and sell them for $7 a piece, the percent markup is 64.2%.

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The sign "%" represents it. To compute a percentage, divide the value by the entire amount and multiply the result by 100. (value/total value)100% is the formula for calculating percentage.

Here,

Total cost=$312.50

Total sell price=7*125

=$875

Markup Price=(875-312.5)/875*100

=0.642*100

=64.2%

The percent markup is 64.2% when they purchase 125 identical stuffed animal for total cost of 312. 50 and sell them for $7 each.

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Answer:

We all must have heard the word “exponential” before. What does this word mean? Exponential means to become more and more rapid in growth. However, in mathematics, it represents a mathematical expression that has one or more exponents. Hence, we know it as an exponential form.

We can say that a thing may increase with an exponential rate when the increase becomes quicker and quicker as the thing which is talked about becomes larger.

Now let us learn more about the exponential form of numbers which is greatly used and applied in mathematics.

The 4th term of an AP is 6 if the um of the 8th and 9th term is -72, The 4th term of an AP is -18.

The sum of 8th and 9th term of an AP is given as -72.

We can use the formula for the sum of any n terms of an AP,

Sn = n/2[2a + (n-1)d]

Where,

a = first term

d = common difference

n = number of terms

Therefore,

-72 = 8/2[2a + (8-1)d]

-72 = 4[2a + 7d]

-18 = 2a + 7d

Subtracting 7d from both the sides,

-18 - 7d = 2a

Dividing both the sides by 2,

(-18 - 7d)/2 = a

a = -18/2 - (7d)/2

a = -9 - (7d)/2

For the 4th term of an AP,

a4 = a + (4-1)d

=-9 - (7d)/2 + 3d

=-9 + 6d

=-9

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Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

Many straightforward inequalities can be resolved by adding, taking away, multiplying, or dividing both sides until the variable is all that remains. However, these factors will shift the direction of inequality: Using a negative number to multiply or divide both sides. switching the left and right sides. When resolving an inequality, you can do one of the following:

• Add the same amount to each side;

• Subtract the same amount from each side;

• Multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.

5 x (23-18) x (8-4)=100

So we can subtract 23 from 18 where we will get 5 and by subtracting 4 from 8 you will get 4. By multiplying the numbers using × operator you will get the final answer.

Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

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Answer:8 cm 6 cm 8 cm 6 cm The perimeter of the shape is 8 + 6 + 8 + 6 = 28cm.

Step-by-step explanation:

The new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5).

What is the Dilation of the rectangle?

Dilation occurs when a polygon grows or shrinks while maintaining its overall shape. It's similar to zooming in or out on a camera. The polygon in the figure above is a rectangle JKLM. As you move the slider on the right, the transformed rectangle J'K'L'M' grows and shrinks but retains its shape.

We have,

Rectangle JKLM with vertices:

J(-6,2), K(-4,4), L(0,0) M(-2,-2): K= 5/2

New dilation vertices of the rectangle are:

J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5)

Hence, the new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0), and M'(-5, -5).

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Answer:

$31

Step-by-step explanation:

x=cost before tax

$32.55 = x + x * 5%  ==> solve for x

$32.55 = x + x * 5/100  

$32.55 = x + 5x/100

$32.55 = 100x/100 + 5x/100 ==> make common denominators

$32.55 = (100x+5x)/100

$32.55 = 105x/100  ==> simplify

100 * $32.55 = 100 * 105x/100  ==> multiply by 100 on both sides to remove

                                                         fractions

$3255 = 105x

x = $3255/105

x = $31

The best measure of central tendency to determine the center of the distribution of teacher salaries is the mean.

The mean is the average of all values in a set and is calculated by adding up all the values and dividing them by the number of values. This measure is particularly useful for data that follows a normal distribution, as teacher salaries are likely to do.

The mean is the most commonly used measure of central tendency and is a good indicator of the center of the data set. It is also relatively easy to calculate. So mean will be the measure of the central tendency to determine the center of the distribution of teacher salaries.

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The iterated integral by converting to polar coordinates [tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] is 7a^4/12.

In the given question, we have to evaluate the iterated integral by converting to polar coordinates.

The given integral is

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex]

Let polar coordinate.

x = rcosθ, y = rsinθ, x^2 + y^2 = r^2

So dxdy = rdrdθ

r from 0 to a and θ from π/2 to π

Now the integral is

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\int_{\pi/2}^{\pi}\int_{0}^{a}7(r\cos\theta)^2(r\sin\theta)drd\theta[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\int_{\pi/2}^{\pi}\int_{0}^{a}7(r^2\cos^2\theta)(r\sin\theta)drd\theta[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\int_{0}^{a}r^3\cos^2\theta\sin\theta drd\theta[/tex]

Now integrating the first integral

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\left[\frac{r^4}{4}\right]_{0}^{a}\cos^2\theta\sin\theta d\theta[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\left[\frac{a^4}{4}-\frac{0^4}{4}\right]\cos^2\theta\sin\theta d\theta[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\frac{7a^4}{4}\int_{\pi/2}^{\pi}\cos^2\theta\sin\theta d\theta[/tex]

Let cosθ = t

So -sinθ = dt/dθ

So sinθdθ = -dt

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\int_{\pi/2}^{\pi}t^2dt[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\left[\frac{t^3}{3}\right]_{\pi/2}^{\pi}[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\left[\frac{\cos^3\theta}{3}\right]_{\pi/2}^{\pi}[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{12}\left[\cos^3\pi-\cos^3(\pi/2)\right][/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = -7a^4/12[(-1)^3 - 0]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = 7a^4/12

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The complete question is:

Evaluate the iterated integral by converting to polar coordinates.

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex]

Answer:

The ball travels (exactly) 75 feet.

Step-by-step explanation:

Assuming the balls comes to rest:

S = a1 / (1 - r)

Now a1 is the first bounce, 20 ft (10 feet up, 10 feet down.

r is 2/3

S = 20 (1 / (1 - 2/3)

S = 20 / (1/3)

S = 60

Yet that is only the bounce. The drop of 15 feet must be added.

The function that matches the graph is f(x) = (17/24)(x + 2)²(x + 6).

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand the behavior of the graph.

As per the given graph,

The function is symmetric at x = -2 so it will be an even degree function as (x + 2)².

The function is not symmetric about x = -6 so it will have an odd degree as (x + 6)¹.

The function will be f(x) = C(x + 2)²(x + 6).

The constant will be C = 17/(2² × 6) = 17/24

Hence "The function that matches is f(x) = (17/24)(x + 2)²(x + 6)".

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The given geometric series [tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex] is convergent in nature.

[tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex]

Since it is geometric series. (As it is given in the question)

A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

Here the value of a=8, while the value of the common ratio [tex](r)=\frac{a_2}{a_1}=\frac{7}{8}=\frac{7}{8}[/tex]

since [tex]$|r|=\frac{7}{8} < 1$[/tex]

So the given series is convergent.

The sum of geometric series with infinite terms is equal to [tex]$\frac{a}{1-r}$$$[/tex]

Sum[tex]=\frac{8}{1-\frac{7}{8}}=\frac{8}{\frac{1}{8}}=64[/tex]

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The time will 90% of the population have heard the rumor are by the time of 3:48 PM.

There are commonly 3 forms of populace pyramids made out of age-intercourse distributions-- expansive, constrictive and stationary.Population is described as all nationals gift in, or briefly absent from a country, and extraterrestrial beings completely settled in a country.

This indicator indicates the variety of humans that typically stay in an area. Growth prices are the yearly adjustments in populace as a result of births, deaths and internet migration at some stage in the year.3000–240=1260

1260 folks heard in four hours=315 folks consistent with hour

90% of populace= 3000 x 0.9= 2700 folks

2700–1500=1200 folks

1200/315=3.eight hours past midday or 3.forty eight pm.

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Answer:

Step-by-step explanation:

105 cm

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis.

What is test statistic?

A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.

A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

The alternative and null hypotheses are listed below.

Lack of hypothesis H0: μ = 13

Ha: 13 Alternative Hypothesis

Statistical test, z = (xbar - mu)/(sigma/sqrt(n))

z = (11 - 13)/(8/sqrt(50))

z = -1.77

Region of Rejection

For α= 0.05, this is a left-tailed test.

Z has a critical value of -1.645.

Therefore, if z -1.645, reject H0 and accept the null hypothesis.

P-value Approach

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis

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Answer:

Step-by-step explanation:

Calculating Average Weekly Pay for Uneven Work Hours Some professions like nurses & doctors in the healthcare industry might work longer shifts where they are on for 12 hours