A store is having a sale with 45% off every item. Which numbers are equivalent to 45%? Select TWO correct answers. 1 45 9 20 2²/²3 5 45 100 20 4/1/2​

Answer:

K5.60.

Step-by-step explanation:

Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

Answer:

There are a total of 25 marbles in the bag.

The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.

Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.

The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.

To find the probability of both events occurring together, we multiply their individual probabilities:

8/25 x 1/8 = 1/25

Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.

Answer:-132

Step-by-step explanation:

The values of independent random variables (a)E(Y), (b)V(Y), (c) E(2Y), and (d) V(2Y) using covariance are 36, 1296, 72, and 5184 respectively.

We can use the following properties of expected value and variance:

E(aX) = aE(X) for any constant a

V(aX) = a² V(X) for any constant a

E(X + Y) = E(X) + E(Y) for any random variables X and Y (assuming they have finite expected values)

V(X + Y) = V(X) + V(Y) + 2Cov(X, Y), where Cov(X, Y) is the covariance between X and Y.

(a) E(Y) = E(6X1 - 6X2) = 6E(X1) - 6E(X2) (by linearity of expectation)

= 6(9) - 6(3) = 36

Therefore, E(Y) = 36.

(b) V(Y) = V(6X1 - 6X2) = 36V(X1) + 36V(X2) - 72Cov(X1,X2) (by the variance formula)

To find the covariance between X1 and X2, we note that they are independent, so Cov(X1, X2) = 0.

Substituting the values of the variances, we get:

V(Y) = 36(6²) + 36(4²) - 72(0) = 1296

Therefore, V(Y) = 1296.

(c) E(2Y) = 2E(Y) (by linearity of expectation)

= 2(36) = 72

Therefore, E(2Y) = 72.

(d) V(2Y) = 4V(Y) (by the variance formula)

= 4(1296) = 5184

Therefore, V(2Y) = 5184.

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It is not possible to calculate the area accurately. If you could provide more details about the figure, such as its shape or a diagram, I would  to help you calculate the area.

Based on the information provided, it seems you are asking for the area of a figure with sides 4, 8, 4, 4, 8, and 16 meters.

However, without knowing the specific shape of the figure,  In general, calculating the area of a shape involves using formulas specific to that shape,

such as length × width for rectangles or base × height × 0.5 for triangles. Once you provide more information about the figure, I can guide you through the appropriate calculation.

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Answer:

16

Step-by-step explanation:

Step 1: Write down the function \(f(x)=7x^2+2x+3.\)

Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)

Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)

Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)

Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)

Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)

Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)

Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)

Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)

The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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let's firstly convert the mixed fractions to improper fractions, and then subtract.

\(\stackrel{mixed}{8\frac{1}{9}}\implies \cfrac{8\cdot 9+1}{9}\implies \stackrel{improper}{\cfrac{73}{9}}~\hfill \stackrel{mixed}{6\frac{7}{8}}\implies \cfrac{6\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{55}{8}}\\\\[-0.35em]~\dotfill\\\\\cfrac{73}{9}-\cfrac{55}{8}\implies \stackrel{\textit{using}\stackrel{LCD}{72}}{\cfrac{(8\cdot 73) - (9\cdot 55)}{72}}\implies \cfrac{584-495}{72}\implies \boxed{\cfrac{89}{72}\implies 1\frac{17}{72}}\)

Answer:

which questions do you want to ask

Step-by-step explanation:

sorry but I didn't know

Answer:

2/(1/4) = 8 1/4th gallons to fill the container and 1/8 * x = 8/8 (x=8) times you can fill the tank with 1/4th gallon

Step-by-step explanation:

First let's answer the first part of the question: what fraction of the container is filled?

If there is 1/4 a gallon of water in the container which holds 2 gallons, we can show this by adding 0/4 to 1/4 to get 1/8 as the fraction of the container filled. (Or just double the denominator for both gallons instead of 1)

To represent this with a multiplication equation, we will take the holding of the container which is 2 gallons

1/8 times x = how many times you can fill the container with 1/4 gallon of water (which is 8 total)

and then our division which is

2 divided by 1/4 = how many shares of water can fit in the container

I hope this helps :)

Answer:

x = 7, y = 45

Step-by-step explanation:

\(7x+13=6x+20\)

\(x=20-13\\x=7\)

Angle

\(7(7)+13=49+13=62^{0}\)

supplementary angle

180 - 62 = 118°

\(3y-17=118\)

\(y=\frac{118+17}{3} =135/3=45\)

Hope this helps

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

To find the horizontal distance between Luke and the kite, we can use trigonometry. The horizontal distance is equal to the length of the string multiplied by the cosine of the angle. Let's calculate it:

Horizontal distance = 400 feet * cos(50°)

Using a calculator, we can find the cosine of 50 degrees to be approximately 0.6428. Multiplying this by 400 feet, we get:

Horizontal distance = 400 feet * 0.6428 ≈ 257.12 feet

Therefore, the horizontal distance between Luke and the kite is approximately 257.12 feet when rounded to the nearest hundredth.

Step-by-step explanation:

Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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The new coordinates of the reflected point will be (2, 2).

In mathematics, reflection is a transformation that "flips" an object over a line or plane. Reflection is a type of symmetry, where an object appears exactly the same after being reflected as it did before.  

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.  

Here we have

The point (-2, 2) is reflected across the y-axis

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.

The new coordinate of the point = (-(-2), 2) = (2, 2)

Therefore,

The new coordinates of the reflected point will be (2, 2).

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The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

A

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Yes it is the variable

Answer:

b=−ax+4a+3x

a= b−3x −x+4

Step-by-step explanation:

The values of a and b make the solution of the equation x = -5 are 1 and -6

The equation is given as:

a(4-x) = -3x+b

When x = -5, we have:

a(4+5) = -3(-5)+b

Evaluate the products

9a = 15 + b

Set a = 1

9(1) = 15 + b

Make b the subject

b = 9 - 15

b = -6

Hence, the values of a and b make the solution of the equation x = -5 are 1 and -6

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The explicit formula for this sequence exists as = (-9) + (n-1)6

We can use an explicit formula, as previously discussed, to determine the nth term in a series. The simplest meaning of explicit is precise or unambiguous. The reason the formula is explicit is that, if properly used, it can be used to find the nth term.

An arithmetic sequence can be expressed explicitly as a = a + (n - 1)d, and each term of the sequence can be computed without knowledge of the other parts. The nth term of an arithmetic, geometric, or harmonic series is usually the explicit formula.

Given: -9, -3, 3, 9, 15. ​

Because it is an arithmetic series, the supplied sequence.

Therefore, there is no difference between two consecutive terms.

For example, 3-(-3)=6 and (-3)-(-9)=6.

The nth term is now equal to a+(n-1)d.

as, a=-9

So, = -9+(n-1)6

= -9+6n-6

= 6n-15

so that =-9+(n-1)6.

The answer is option D

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Answer:

Domain (-4,6)

Range(5,0)

Step-by-step explanation:

Answer:

\(f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right), \quad \textsf{for}\:\{x:0 < x < 1\}\)

Step-by-step explanation:

Given function:

\(f(x)=\dfrac{e^x}{\sqrt{e^{2x}+1}}\)

The domain of the given function is unrestricted:  {x : x ∈ R}

The range of the given function is restricted:  {f(x) : 0 < f(x) < 1}

To find the inverse of a function, swap x and y:

\(\implies x=\dfrac{e^y}{\sqrt{e^{2y}+1}}\)

Rearrange the equation to make y the subject:

\(\implies x\sqrt{e^{2y}+1}=e^y\)

\(\implies x^2(e^{2y}+1)=e^{2y}\)

\(\implies x^2e^{2y}+x^2=e^{2y}\)

\(\implies x^2e^{2y}-e^{2y}=-x^2\)

\(\implies e^{2y}(x^2-1)=-x^2\)

\(\implies e^{2y}=-\dfrac{x^2}{x^2-1}\)

\(\implies \ln e^{2y}= \ln \left(-\dfrac{x^2}{x^2-1}\right)\)

\(\implies 2y \ln e= \ln \left(-\dfrac{x^2}{x^2-1}\right)\)

\(\implies 2y(1)= \ln \left(-\dfrac{x^2}{x^2-1}\right)\)

\(\implies 2y= \ln \left(-\dfrac{x^2}{x^2-1}\right)\)

\(\implies y= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right)\)

Replace y with f⁻¹(x):

\(\implies f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right)\)

The domain of the inverse of a function is the same as the range of the original function.  Therefore, the domain of the inverse function is restricted to {x : 0 < x < 1}.

Therefore, the inverse of the given function is:

\(f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right), \quad \textsf{for}\:\{x:0 < x < 1\}\)

Answer:

Step-by-step explanation:

The correct  equation is D. x2 + y2 + 6x − 24y + 148 = 0.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.


This equation is the general form of a circle with center A and radius 5. The equation can be derived from the coordinates of the center A and the radius of the circle. The center of the circle is located at (-3, 12). To get the equation, first calculate the distance between the center A and a point on the circumference of the circle, which is the radius of the circle, 5. Then, use the Pythagorean theorem to calculate the equation of the circle: x2 + y2 + 6x – 24y + 148 = 0.
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The definite integral for this problem has the result given as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}\)

The definite integral for this problem is defined as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx\)

We have an integral of the sum, hence we can integrate each term, and then add them.

For the first two terms, applying the power rule, the integrals are given as follows:

The integral of the tangent is given as follows:

ln|sec(x)|

Then the integral is given as follows:

I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.

Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:

I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)

I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 212 - ln|sec(5)| + ln|sec(1)|.

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Answer:

Step-by-step explanation:

true

Probability of an event is the measure of its chance of occurrence. The probability that the family has 0,1 or 2 girls is 0.7504

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

\(X \sim B(n,p)\)

The probability that out of n trials, there'd be x successes is given by

\(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

For two events A and B, we have:

Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.

This can be written symbolically as:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

For three events, A, B and C:

\(P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A\cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)\)

For the given case,

If the random variable  X is such that:

X = number of girls born to a family which has two children.

Then, we can model this situation by Binomial distribution, where Bernoulli experiment is birth of child which either results in being girl(call it success), or boy( call it failure) (in this case, we assume that only two gender exist).

Since total there are 2 children, so n = 2

In that specified family, success  in Bernoulli experiment  = birth of girl, so probability of success = P(birth of girl)  = 0.48 = p

and, failure in Bernoulli experiment = birth of boy, thus, probability of failure = P(birth of boy) = 0.52 = q = 1-p

Thus, X pertains binomial distribution (as it is count of successes), as:

\(X \sim B(n = 2,p = 0.48)\)

Evaluating the needed probabilities:

Using the probability function for binomial distribution, we get:

\(P(X = 0) = \: ^2C_0(0.48)^0(0.52)^2 = 0.2704\\\)

Using the probability function for binomial distribution, we get:

\(P(X = 0) = \: ^2C_1(0.48)^1(0.52)^1 = 0.2496\\\)

Using the probability function for binomial distribution, we get:

\(P(X = 0) = \: ^2C_2(0.48)^2(0.52)^0 = 0.2304\\\)

If we take three events as:

Then, their simultaneous occurrence isn't possible, so the probability of their intersection isn't possible.

The probability of event of getting 0, 1 or 2 girl child in that family is written as: \(P(A \cup B\cup C)\). Using the addition rule, and knowing that their intersection is having 0 chances, thus,

\(P(A \cup B \cup C) = P(A) + P(B) + P(C) =\) \(0.2704 + 0.2496 + 0.2304 = 0.7504\)

Thus, he probability that the family has 0,1 or 2 girls is 0.7504

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Answer:

To calculate the book value of the building, we need to calculate the annual depreciation amount and multiply it by the number of years elapsed since the building was completed.

The annual depreciation amount is calculated as: $1 million / 50 years = $20,000

In 2014, the book value of the building was: $1 million - ($20,000 * (2014 - 2010)) = $1 million - ($20,000 * 4) = $960,000

In 2022, the book value of the building will be: $1 million - ($20,000 * (2022 - 2010)) = $1 million - ($20,000 * 12) = $680,000