The expression 3r - 6 can be written as _____. 3(r - 2) 3(r - 6) 3(3r - 6).

Answer:

===========================

The amount of simple interest is:

or

Given:

Substitute and calculate:

The matching choice is D.

Answer:

$46,800

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for I:

\(\implies \sf I=60000(0.065)(12)\)

\(\implies \sf I=3900(12)\)

\(\implies \sf I=46800\)

Therefore, the interest is $46,800.

Answer & Step-by-step explanation:

4(t + 2) = 10

4t + 8 = 10

4t = 2

t = 1/2

Hope this helps

Answer:

Sam is right.

Step-by-step explanation:

Key skills needed: Fraction Modelling, Fraction Division

1) We are given this problem --> \(6\) ÷ \(\frac{1}{4}\)

2) This means we need to find how many \(\frac{1}{4}\)'s are in 6.

3) There are 2 ways to approach this problem

        1. The first way is via using the fractional division properties:

Let's say we are given a problem --> \(a\) ÷ \(\frac{b}{c}\)

This can be made into  --> \(a\) × \(\frac{c}{b}\)

It is a simple property that should be remembered.

This means that \(6\) ÷ \(\frac{1}{4}\) is the same as \(6\) × \(\frac{4}{1}\) which is 24.

        2. The second way is with using a model (which I am not very good with). The model way is the image I will post.

Hope you understand both ways and have a nice day!! :D    

The equations with same value of x as (3/5)(30x - 15) = 72 is 18x - 9 = 72, 3(6x - 3) = 72 and x = 4.5

An equation shows the relationship between two or more numbers and variables.

Given the equation:

(3/5)(30x - 15) = 72

Opening the parenthesis:

18x - 9 = 72

Factorizing the equation:

3(6x - 3) = 72

Dividing through by 3:

6x - 3 = 24

6x = 27

Dividing through by 6:

x = 4.5

The solution to the equation (3/5)(30x - 15) = 72 yields x = 4.5

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Answer:

Step-by-step explanation: false

It is true that if BD bisects ∠ABC, then D lies in the interior of ∠ABC

There are three types of triangle and they are

Isosceles triangle in which two sides and two angles are same.

Equilateral triangle in which all the sides and angles are equal.

Scalene triangle in which none of the sides and angles are equal.

According to the given question

If BD bisects ∠ABC, then D lies in the interior of ∠ABC and it is true.

If we draw any line from the vertex B which passes through inside the given triangle then it lies in the interior of \(\angle B\).

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The two-dimensional heat equation aU_xx + aU_yy = U must be substituted into the equation and checked to see whether it still holds in order to prove that the function '(U(x,y;t) = e-aomega t'cos(x)sin(y)' is a solution.

The partial derivatives of (U) with respect to (x) and (y) are first calculated as follows:

\[U_x = -e-a-omega-t-sin(x,y)]

[U_y = e-a omega t cos(x,y)]

The second partial derivatives are then computed:

\[U_xx] is equal to -eaomega tcos(x)sin(y).

[U_yy] = e-a omega tcos(x), sin(y)

Now, when these derivatives are substituted into the heat equation, we get the following result: [a(-e-aomega tcos(x)sin(y)) + a(-e-aomega tcos(x)sin(y)) = e-aomega tcos(x)sin(y)]

We discover that the equation is valid after simplifying both sides.

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The shape of the sampling distribution of sample means from a sample of size 100 taken from a bimodal distribution of Red Delicious apple diameters with a mean of 2.63 in. and a standard deviation of 0.25 in. is approximately normal.

According to the central limit theorem, when the sample size is sufficiently large (typically greater than 30) and the population distribution is not severely skewed, the sampling distribution of sample means tends to approximate a normal distribution, regardless of the shape of the population distribution.

In this case, even though the population distribution of Red Delicious apple diameters is bimodal, the sample size of 100 is considered large enough for the central limit theorem to apply. As a result, the sampling distribution of sample means will be approximately normal.

This means that if we were to take multiple random samples of size 100 from the orchard and calculate the mean diameter for each sample, the distribution of those sample means would be bell-shaped and follow a normal distribution.

Therefore, the shape of the sampling distribution of sample means from the given sample size and population distribution is approximately normal.

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1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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The probability that at most two customers purchase the investment is 0.1875 or 18.75%.

To calculate the probability that at most two customers purchase the investment,  to calculate the probabilities for each possible outcome: 0, 1, and 2 customers purchasing the investment, and then sum them up.

Let's consider the customers as A, B, C, and D, with D being the fourth customer.

Probability of 0 customers purchasing:

P(0 customers) = (1 - probability of sale)²number of customers

= (1 - 0.5)²4

= 0.0625

Probability of 1 customer purchasing:

P(1 customer) = (probability of sale)²1 ×(1 - probability of sale)²3 (since 3 customers won't purchase)

= 0.5²1 ×0.5²3

= 0.5 × 0.125

= 0.0625

Probability of 2 customers purchasing:

P(2 customers) = (probability of sale)²2 × (1 - probability of sale)²2 (since 2 customers will purchase)

= 0.5²2 ×0.5²2

= 0.25 × 0.25

= 0.0625

Now  sum up these probabilities to find the probability that at most two customers purchase the investment:

P(at most 2 customers) = P(0 customers) + P(1 customer) + P(2 customers)

= 0.0625 + 0.0625 + 0.0625

= 0.1875

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Answer:

It is closer to 1.

Step-by-step explanation:

Think about this:

1 1/4 is 1/4 closer to one.

1 1/4 is 3/4 closer to two.

Answer:

1

Step-by-step explanation:

1 1/4 can be represented as 1.25 as a decimal.

Any decimal that is 1.5 or is higher will round up to 2, and anything that is 1.49 or lower will round down to 1.

No, your friend is not correct. The output does not equal the input divided by 2.

Looking at the table, we can see that the output values do not follow a consistent pattern of being equal to the input values divided by 2. In order to determine if the friend's claim is correct, we need to examine the relationship between the input and output values for each entry in the table.

If we divide the input values by 2 and compare them to the corresponding output values, we can see that they do not match. For example, when the input is 4, the output is 3; however, 4 divided by 2 is equal to 2, not 3. Similarly, when the input is 6, the output is 4, but 6 divided by 2 is equal to 3, not 4.

Therefore, based on the given table, it is clear that the output values are not obtained by dividing the input values by 2. There must be another pattern or relationship governing the output values, which is different from simple division by 2.

To determine the correct pattern, we need to analyze the table further and identify any consistent rules or formulas that govern the relationship between the input and output values. It is possible that there is a different mathematical operation or formula involved that produces the given output values. Further investigation and analysis are necessary to determine the actual pattern or relationship in the table.

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Answer:

450miles

Step-by-step explanation:

Because she is riding at 20 miles per houre means that she ride 450 miles in 5 houre.

The probability that a tick carries Lyme disease given that it carries hge is approximately 0.0788.

The conditional probability of an event depending on the occurrence of another event, according to Bayes' Theorem, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.

Let's use Bayes' theorem to calculate the probability of a tick carrying Lyme disease given that it carries hge.

Let A be the event that a tick carries Lyme disease and B be the event that a tick carries hge. We want to find P(A|B), the probability that a tick carries Lyme disease given that it carries hge.

Bayes' theorem states:

P(A|B) = P(B|A) * P(A) / P(B)

Given,

P(A) = 0.14 (the proportion of ticks that carry Lyme disease)

P(B) = 0.08 + 0.08 - 0.08*0.08 = 0.1432 (the proportion of ticks that carry hge)

The probability of a tick carrying hge is 0.08, and the probability of a tick carrying Lyme disease given that it carries hge is 0.08*0.08 = 0.0064, so we need to subtract this from 0.08 to avoid double-counting ticks that carry both diseases.

P(B|A) = 0.08 (the proportion of ticks that carry hge given that they carry Lyme disease)

Plugging in these values:

P(A|B) = 0.08 * 0.14 / 0.1432 ≈ 0.0788

Therefore, the probability that a tick carries Lyme disease given that it carries hge is approximately 0.0788, rounded to four decimal places.

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Answer:

1.......c

2.....a

3.....b

4......e

5.....d

Because of the size of the black section,

Answer:

I think its 7330

A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Answer:

3

Step-by-step explanation:

1/3 x (9/1) = 3

Answer:

Yes

Step-by-step explanation:

Answer:

y = 2x+2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the y-intercept first, then, from that point, go tide over run to find your slope. This line has a positive slope, so count up two and over one (2/1). After that, input what data you've collected into your equation (y = mx + b) and you'll have your answer.

The components of the curl of F are 0, cos(x), and 0.

curl(F) = cos(x) j

We have,

The curl of the vector field F is given by:

curl(F) = (∂Q/∂y - ∂P/∂z) i + (∂P/∂z - ∂R/∂x) j + (∂R/∂x - ∂Q/∂y) k

where P, Q, and R are the components of F.

In this case, we have:

P(x,y,z) = x sin(y)

Q(x,y,z) = -y cos(x)

R(x,y,z) = yz^2

So, we need to compute the partial derivatives:

∂P/∂z = 0

∂Q/∂y = -cos(x)

∂R/∂x = 0

∂P/∂y = x cos(y)

∂Q/∂z = 0

∂R/∂y = z^2

∂P/∂x = sin(y)

∂Q/∂x = y sin(x)

∂R/∂z = 2yz

Now,

curl(F) = (0 - 0) i + (0 + cos(x)) j + (0 - 0) k

= cos(x) j

So the components of the curl of F are 0, cos(x), and 0.

Thus,

The components of the curl of F are 0, cos(x), and 0.

curl(F) = cos(x) j

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The speed of the moving body that is being referred to here is 80 kilometer per hour.

The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.

                                \(Distance = speed * time\)

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Answer:

5n

Step-by-step explanation:

:)

Answer:5n

Step-by-step explanation:

Answer:

x=60+70=130(exterior angle of a triangle is equal to the sum of two opposite interior angle)

To find the distance between two points on a coordinate plane, we can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

In this case, the two points are (4, 7) and (11, -1) , so we have:

d = √((11 - 4)^2 + (-1 - 7)^2)

d = √((7)^2 + (-8)^2)

d = √(49 + 64)

d = √113

Therefore, the distance between the two points on the coordinate plane is c = √113 (approximately 10.6)

You can round to the nearest tenth, so the distance c = 10.6.

Answer:

-------------------------------------

Use the distance formula to find the distance between the given points:

Substitute coordinates and calculate:

The probability of x = 2 when x ∼ bin(4,0.8) is 0.1536.

The probability of x = 2 when x ∼ bin(4,0.8) can be calculated using the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where n is the number of trials, x is the number of successes, and p is the probability of success on a single trial.

In this case, n = 4, x = 2, and p = 0.8.

P(x = 2) = (4 choose 2) * 0.8^2 * (1-0.8)^(4-2)

P(x = 2) = (6) * 0.64 * 0.04

P(x = 2) = 0.1536

Therefore, the probability of x = 2 is calculated when x ∼ bin(4,0.8) is 0.1536.

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Yes, this fact would make you suspect that the loader had slipped out of adjustment.

If the average weight of the cars is below 85.5 tons, then the weight of some of the individual cars must have been lower than 85.5.

This suggests that the coal hadn't been evenly loaded into the cars, which could be an indication that the loader was out of adjustment.

Furthermore, low weights in some of the cars could also suggest that there was an issue with accuracy in the loader, as it might not have been loading the correct amount of coal per car.

Yes, this fact could make you suspect that the loader had slipped out of adjustment.

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Answer:

Function A  intercept: 4

Function B intercept: 3

Step-by-step explanation:

Answer:

9/8

Step-by-step explanation:

3/16 x 6

= 3/16 x 6/1

= 18/16

= 9/8

The length of a rectangle is three inches less than five times the width. The perimeter is 18 inches. To find: Length and width of the rectangle.

Let's assume that the width of the rectangle be w. The length of the rectangle is three inches less than five times the width. Therefore, the length will be (5w - 3). The perimeter of the rectangle is 18 inches, which can be calculated using the formula: P = 2l + 2w where l is the length and w is the width. Substituting the given values we get,
18 = 2(5w - 3) + 2w18 = 10w - 6 + 2w18 = 12w - 618 + 6 = 12w12 = 12w/12w = 1
Therefore, the width of the rectangle is 1 inch. The length of the rectangle is (5w - 3), which is equal to
5(1) - 3 = 2 inches. Therefore, the length of the rectangle is 2 inches and the width of the rectangle is 1 inch.

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Answer:

fg(-2)=17

Step-by-step explanation:

fg(x)=4(-2x)+1

=-8x+1

fg(-2)=-8(-2)+1

=16+1

17