Simplify the product using the Distributive Property.

(4r –5)(7r + 2)
A. 28r2 + 43r – 10
B. 28r2 – 27r + 10
C. 28r2 + 43r + 10
D. 28r2 – 27r – 10

Answer:

=7x2+6x+4

Step-by-step explanation:

3x+7x2+2x+3+x+1

Combine Like Terms:

=3x+7x2+2x+3+x+1

=(7x2)+(3x+2x+x)+(3+1)

=7x2+6x+4

Answer:

=7x2+6x+4

Answer:

∠F = 19.5

Step-by-step explanation:

180 - 127 - 33.5 = 19.5

Answer:

m∠LPM = 60°

Step-by-step explanation:

The 95% confidence interval for the slope of the regression line in this case is 0.74 ± 0.242.

To calculate the confidence interval for the slope of the regression line, we need to consider the standard error of the slope (sb) and the critical value associated with the desired confidence level.

Given that the standard error of the slope (sb) is 0.11, we can calculate the critical value using the t-distribution with a confidence level of 95% and degrees of freedom equal to the number of observations minus the number of variables in the regression (12 - 2 = 10).

Looking up the critical value in the t-distribution table or using a statistical calculator, the critical value for a 95% confidence level with 10 degrees of freedom is approximately 2.228.

The margin of error for the slope can be calculated by multiplying the critical value by the standard error: 2.228 * 0.11 = 0.245.

Therefore, the 95% confidence interval for the slope is 0.74 ± 0.245. This means we are 95% confident that the true slope of the regression line falls within the range of 0.495 to 0.985.

Among the options provided, the closest match is option (b): 0.74 ± 0.242.

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Answer:

1

Step-by-step explanation:

0.81666666666

Answer:

5/12+2/5

That is the answer as the real decimal is 0.81666 repeating

Step-by-step explanation:

Answer:

A) 1

Step-by-step explanation:

Using the angle addition postulate,

\(79x-1+53x+1=132 \\ \\ 132x=132 \\ \\ x=1\)

Answer:

0

Step-by-step explanation:

Answer: A triangular prism has a base of a rectangle as shown in this picture.

Step-by-step explanation: If your having trouble recognizing prisms here's a tip. All prisms have a rectangular base. :)

Answer:

you cant tell

Step-by-step explanation:

it depends how many if each button

in there is

Answer:

-12 - 10i.

Step-by-step explanation:

-9 - 8i - (3 + 2i)

= -9 - 8i - 3 - 2i

= -12 - 10i.

Answer:

58

Step-by-step explanation:

1 isn't a prime number. 2 is the smallest, which is in 58

it is not possible for det A to equal 3 if the entries of both A and A^-1 are integers.

The determinant of a matrix and its inverse are multiplicative inverses of each other, meaning that det(A)det(A^-1) = 1. If det A = 3, then det(A^-1) = 1/3. However, since the entries of both A and A^-1 are integers, this is a contradiction, as the determinant of a matrix with integer entries must also be an integer. Therefore, it is impossible for det A to equal 3 in this scenario.

it explains the reasoning behind the solution and provides a deeper understanding of the concept of determinants.

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The fourth quintile based on the given sample observations is approximately 15.5.

To find the fourth quintile, we first need to arrange the sample observations in ascending order:

-31, 9, 13, 18, 24

The fourth quintile represents the value below which 80% of the data falls. Since we have 5 data points, the fourth quintile is located at the 80th percentile, which can be calculated as:

80th percentile = (80/100) * (n + 1) = (80/100) * (5 + 1) = 4.8

Since the 80th percentile falls between the fourth and fifth observations, we can estimate the fourth quintile by taking the average of these two values:

Fourth quintile ≈ (13 + 18) / 2 = 15.5

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The multiplier for the given economy is 4.

The multiplier represents the magnification effect of an initial change in autonomous spending on the overall output of an economy. It is calculated using the formula 1 / (1 - MPC), where MPC is the marginal propensity to consume.

In this case, the MPC is given as 0.75, which means that for every additional dollar of income, individuals spend 75 cents. The multiplier is calculated as 1 / (1 - 0.75) = 4.

The multiplier of 4 indicates that a change in autonomous spending, such as investment or consumption, will have a four times larger impact on the overall output of the economy. In other words, for every dollar increase in autonomous spending, the total output of the economy will increase by four dollars.

In this scenario, since the intended investment is $130, the total increase in output would be 4 * $130 = $520. Therefore, the multiplier effect amplifies the initial change in autonomous spending and leads to a larger increase in output in the economy.

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Answer:

Cluster analysis is used to identify groups of entities that have similar characteristics is a true statement.

Step-by-step explanation:

Cluster analysis is a statistical technique used to identify groups or clusters of entities that exhibit similar characteristics or behaviors. It is a common method employed in data mining, machine learning, and exploratory data analysis.

The goal of cluster analysis is to group data points or entities in a way that maximizes the similarity within each cluster and minimizes the similarity between different clusters. The similarity or dissimilarity between data points is typically measured using a distance or similarity metric, such as Euclidean distance or correlation coefficient.

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Answer:

3,400 grams

Step-by-step explanation:

The total amount of flour needed to make two batches of each recipe is 3400 grams.

1000 grams is equal to 1 kilogram.

Amount of flour used in one batch of the first recipe= 1 kilogram

So, the amount of flour used in two batches of the first recipe=2 kilogram =2000 grams.

Amount of flour used in one batch of the second recipe= 700 grams

So, the amount of flour used in two batches of the second recipe= 2*700=1400 grams.

Total amount of flour needed = 2000+1400 =3400 grams.

Hence, The total amount of flour needed to make two batches of each recipe is 3400 grams.

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Answer:

=49x+65y

Step-by-step explanation:

Answer:

49x+65y

Step-by-step explanation:

Only the x can be added to the x and only the y can be added to the y.

So 20+29=49 then add an x

27+38=65 then add a y

Always put your answer in alphabetical order.

The value of the given integral by converting it into polar coordinates is [a⁴ / 4] (1 - (-1)) = [a⁴ / 2].Hence, the correct option is (d) [a⁴ / 2].

To evaluate the iterated integral by converting to polar coordinates,

we need to change the limits of the integral into polar coordinates.

So the given integral in polar form is ∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0)\(4r^3cos(θ)sin(θ)dr dθ.\)

The polar coordinate conversion is given by x = r cos(θ) and y = r sin(θ).Given integral ∫a0∫0−√a2−y24x2y dx dy can be expressed in the form of polar coordinates as follows:

∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr dθ

Where, x = r cos(θ) and y = r sin(θ)

Now, we can evaluate this integral using the polar coordinate conversion.

∫(from θ = 0 to θ = π/2)

∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr

dθ=∫(from θ = 0 to θ = π/2) [cos(θ)sin(θ) ∫(from r = a to r = 0) 4r³ dr ]

dθ= ∫(from θ = 0 to θ = π/2) [ cos(θ) sin(θ) (r⁴) / 4] (from r = a to r = 0)

dθ=∫(from θ = 0 to θ = π/2) [cos(θ) sin(θ) (a⁴) / 4]

dθ= [a⁴ / 4] ∫(from θ = 0 to θ = π/2) sin(2θ)

dθ= [a⁴ / 4] ([- cos(2θ)] from θ = 0 to θ = π/2)

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Answer:the coefficient of the 2nd term is : 24

Step-by-step explanation:(6p + 2)^2 =

(6p + 2)(6p + 2) =

36p^2 + 12p + 12p + 4 =

36p^2 + 24p + 4

Answer:

Given

Step-by-step explanation:

When the base is same but the exponents are different, the rule is that a^m/a^n

= a^m-n

So in this case let a be 5, m be 3 and n be 7

5^3/5^7

= 5^3-7

= 5^-4

Solution:

Given a triangle;

Where

To find the measure of angle S, i.e.

Where

Then,

Recall that;

Hence, the measure of angle S is 55°

Answer:

1. (-94)

2. (+3)

Step-by-step explanation:

Hope this helps!!

Step-by-step explanation:

As you can see in first expression both have " - " sign infront of them....so all uh need to do is put that minus sign there and add expression cuz ( - ) and ( - ) will be ( + )

= - 94

In second expression the question

- 1 - ( - 4 )

As we know ( - ) × ( - ) will be ( + ) as it is multiplied so we need to change the sign

- 1 + 4 .............[ ( - ) and ( + ) = ( - ) ] so we need to subtract but the plus sign here has greater number so the sign will be plus ....

= + 3

\(...\)

Answer:

C

Step-by-step explanation:

tr+1=7(1+r) Step 1: Add -7r to both sides. rt+1+−7r=7r+7+−7r rt−7r+1=7 Step 2: Add -1 to both sides. rt−7r+1+−1=7+−1 rt−7r=6 Step 3: Factor out variable r. r(t−7)=6 Step 4: Divide both sides by t-7. r(t−7) t−7 = 6 t−7 r= 6 t−7 Answer: r= 6 t−7

Hoped I helped

By taking the average of her balance of each day of August, we will see that the average daily balance is $373.08

We know that:

So, first, her balance is $579.53 for 7 days. Then her balance is $79.53 for 8 days, then her balance was $279.53 for another 8 days, and finally, her balance was $579.53 for the last 8 days of august.

Then over the 31 days of August, the average daily balance will be:

\(A = \frac{7*579.53 + 8*79.53 + 8*279.53 + 8*579.53}{31} = 373.08\)

So in August, her average daily balance was $373.08

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The pH of the given solution is 2.39.The pH of the given solution can be determined as follows: Concentration of acid, [HA] = 0.914 M.

Percentage ionization of the acid, α = 4.09%

Expression for degree of ionization of a weak acid is given as follows:α = [H+]/[HA] × 100 …

(i)This expression is a result of the ionization equilibrium of the weak acid, which is given as follows:

HA + H2O ⇌ H3O+ + A-Where, HA represents the weak acid, H2O represents water, H3O+ represents hydronium ion and A- represents the conjugate base of the acid.

Using the expression of degree of ionization of the acid given in equation (i), the concentration of hydronium ion can be calculated as follows:

[H+]/[HA] × 100 = 4.09/100⇒ [H+]/[HA] = 0.0409/100

Taking negative logarithm of both sides of the above equation and solving for pH, we get:

pH = - log[H+]

= - log(0.0409/100)

= 2.39

Therefore, the pH of the given solution is 2.39.

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Answer:

C

Step-by-step explanation:

Answer:-i

Step-by-step explanation: :)

Power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x=1.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

The given equation: \(\left(x^2-2 x+26\right) y^{\prime \prime}+x y^{\prime}-4 y=0\)

It is necessary to determine the power series solutions' minimal radius of convergence R around the typical points x = 0 and x = 1.

The separation between the ordinary point and the differential equation's singularity is now the minimal radius of convergence.

The polynomial's root, which is connected to the second derivative, is the singularity point.

The singularity points will be determined as follows:

\(\begin{aligned}& x^2-2 x+26=0 \\& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\& x=\frac{2 \pm \sqrt{(-2)^2-4 \times 1 \times 26}}{2} \\& x=1 \pm \sqrt{-100} \\& x=1 \pm 10 i\end{aligned}\)

In this case, x1 = 1+10i and x2 = 1-10i are the singularity sites.

The ordinary points at this time are z1 = 0+01 and z2 = 1+0i.

One can compute the minimum radius of convergence using the formula:

\(\begin{aligned}& r_1=\left|z_1-x_1\right| \\& =|0+0 i-1-10 i| \\& =\sqrt{101} \\& =10.0498 \\& r_2=\left|z_2-x_1\right| \\& =\sqrt{100} \\& =10\end{aligned}\)

Therefore, power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x = 1.

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Answer:

klfajndxjfasisfcbweauorfochwszhfshsfqsahfwhnlsljfjlashegfchdhefgwsdgrvefdcgbvdqjejjsjjjdkdkk112132w434

Step-by-step explanation:

5uwsuhsrhudhusfhushzoihflishhghwslhkfwdilhtfhwhshfhhwajzhfshadzkhfcshfuhu3eyryyaurjfsdajsfjfjdgagdgsgafdfzdUDSIUIYAYIODQALHPOEPOWIAYISDHAZAHDCGUQEIUSD8RFHGSHXARAGIUROIHTNDAUFCISBQ3AYHQWEID

Answer:

3 meter

Step-by-step explanation: it ez