A small corporation borrowed $500,000 to expand its software line with
an interest $43,500. Some of the money was borrowed at 8%, some at
9%, and some at 10%. The amount borrowed at 8% was two and half
times the amount borrowed at 10%. How much did the corporation invest
at 9% interest? (Write only the amount.)

Answer:

22

Step-by-step explanation:

c²= a²+b²= (5.6)²+ (7,1)²=9

P=5.6+7.1+9=21,7=22

The Solomon four-group design includes two control groups: one that is not pretested and does not receive treatment, and another that is not pretested but receives treatment.

In the Solomon four-group design, there are two treatment groups and two control groups. The purpose of this design is to examine the interaction effect between pretesting and treatment.

The first control group does not receive any treatment, while the second control group also does not receive treatment but is pretested. These two control groups help to measure the impact of pretesting on the dependent variable.

The two treatment groups receive the treatment being studied, with one group being pretested and the other group not being pretested. By comparing the pretested and non-pretested treatment groups, researchers can determine if there is an interaction effect between pretesting and the treatment.

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Answer:

MQ=4... sides are equal

PQ=MQ+MP

=4+4

=8

Answer:

multiply first equation with 3 and second equation with 5

Answer: in 340 million square miles there are 8.808 x 10^10 hectares

Step-by-step explanation:

Answer: x = -5

Step-by-step explanation:

4−2(x+7)=3(x+5)4-2(x+7)=3(x+5)Simplify 4−2(x+7)4-2(x+7).Tap for more steps...−2x−10=3(x+5)-2x-10=3(x+5)Simplify 3(x+5)3(x+5).Tap for more steps...−2x−10=3x+15-2x-10=3x+15Move all terms containing xx to the left side of the equation.Tap for more steps...−5x−10=15-5x-10=15Move all terms not containing xx to the right side of the equation.Tap for more steps...−5x=25-5x=25Divide each term in −5x=25-5x=25 by −5-5 and simplify.Tap for more steps...x = −5

Answer:b

Step-by-step explanation:

The associative property for the expression is  (6 • 1/3)7/5.

Certain rules that are used while multiplying numbers are known as the characteristics of multiplication. All types of mathematical expressions, whether they be algebraic expressions, fractions, or integers, can be solved thanks to these features, which make it simple to simplify expressions.

Given expression 6(1/3 • 7/5),

to write its associative property

The Associative Property of Multiplication states that altering the way the numbers are grouped has no impact on the result of the multiplication.

a(b . c) = (a . b)c

6(1/3 • 7/5) =  (6 • 1/3)7/5

Hence correct expression for the property is option B,  (6 • 1/3)7/5.

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It is simpler to compute the likelihood of the complement event when calculating probabilities since you can then just subtract it from 1 to determine the probability.

the variety of strategies for success. all events that could possibly occur.

Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.

P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).

where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.

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P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. It is simpler to compute the likelihood of the complement event when calculating probabilities.

the variety of strategies for success. all events that could possibly occur.

Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.

P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).

where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.

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We can write the arithmetic sequence as -

{2, 4, 6, 8, 10, 12, ....} and the graph of the function is attached.

Given is to write a function that represents the arithmetic sequence.

       {a, a + d, a + 2d, a + 3d, .....}.

       {2, 4, 6, 8, 10, 12, ....}.

Therefore, we can write the arithmetic sequence as -

{2, 4, 6, 8, 10, 12, ....} and the graph of the function is attached.

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The value of (x,y) is  (1.2 , -4.7) , Option D is the right answer.

The complete question is

On a coordinate plane, a line is drawn from point a to point b. point a is at (7, negative 2) and point b is at (negative 8, negative 9). what are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)

Coordinates are the location of a point in an (x,y) plot.

The given data is

Coordinates of

A = (7,-2)

B = (-8,-9)

m:n = 5:8

The coordinates of partition has to be determined

The formula used is

\(\rm (x,y) = \dfrac{1}{m+n} *(nx_1 + mx_2 , ny_1+ny_2)\\\\\\\rm (x,y) = \dfrac{1}{5+8} *(5*-8 + 8*7 , 5*-9+8*-2)\)

(x,y ) = (1.2 , -4.7)

Therefore Option D is the correct answer.

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Answer:

x=43

Step-by-step explanation:

supplementary angles add up to 180. Therefore 89+2x+5=180.2x=180-94

2x=86 and x is therefore 43.

Answer:

x=43

Step-by-step explanation:

supplementary angles add up to 180. Therefore 89+2x+5=180.2x=180-94

2x=86 and x is therefore 43.

Given: AC and BD bisect each other

AC and BD are intersects at the point E

So, BE = DE and AE = CE

For the triangles : BEC and DEA

1. BE = DE (proved)

2. m∠ BEC = m∠DEA ( vetical angles are congruent )

3. AE = CE ( proved )

So, the triangles are congruent by SAS [ side - angle - side ]

The additional statements that would give enough information to conclude that the door frame forms a rectangle is A. The door frame has a right angle and C. The door frame has a pair of congruent opposite angles.

A rectangle has four right angles, so if you know that the door frame has at least one right angle, then you can conclude that it is a rectangle.

A rectangle also has two pairs of congruent opposite angles, so if you know that the door frame has a pair of congruent opposite angles, then you can conclude that it is a rectangle.

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Full question is:

You are building a door frame. Both sides are 80.5 inches long and the top and bottom are both 36.5 inches wide. Which additional statement(s) give enough information to conclude that the door frame forms a rectangle?

Options

The door frame has a right angle.

The diagonals of the door frame are congruent.

The door frame has a pair of congruent opposite angles.

The door frame has a pair of congruent adjacent angles.

Counting to 20 in Spanish is a relatively straightforward process. The first step is to learn the numbers from 1 to 10, which are:

1 - uno

2 - dos

3 - tres

4 - cuatro

5 - cinco

6 - seis

7 - siete

8 - ocho

9 - nueve

10 - diez

Once you have these numbers memorized, it's easy to continue counting up to 20. Simply add the numbers from 11 to 19 to the base number, diez.

11 - once (diez + uno)

12 - doce (diez + dos)

13 - trece (diez + tres)

14 - catorce (diez + cuatro)

15 - quince (diez + cinco)

16 - dieciséis (diez + seis)

17 - diecisiete (diez + siete)

18 - dieciocho (diez + ocho)  

19 - diecinueve (diez + nueve)

20 - veinte

As you can see, the only exception is the number 15, which has its own unique word, "quince." Other than that, all of the numbers from 11 to 19 follow the same pattern of adding "diez" to the appropriate digit. And once you reach 20, you're done! It's important to note that Spanish has gendered nouns, so when counting objects, you will need to use the appropriate article and adjective to match the gender of the noun. For example, if you are counting "dogs," you would say "uno perro," but if you were counting "cats," you would say "una gata."

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Answer:

1  uno

2  dos

3  tres

4  cuatro

5 cinco

6 seis

7 siete

8 ocho

9 nueve

10 diez

11 once

12 doce

13 trece

14 catorce

15 quince

16 dieciséis

17 diecisiete

18 dieciocho

19 diecinueve

20 veinte

Step-by-step explanation:

(a) Assuming equiprobability, the probability of picking a white ball from Urn I is the ratio of the number of white balls to the total number of balls in Urn I:

P(white ball from Urn I) = 3 / (3 + 4) = 3/7

Similarly, the probability of picking a white ball from Urn II is:

P(white ball from Urn II) = 2 / (2 + 6) = 2/8 = 1/4

(b) After picking a ball randomly from Urn I and placing it in Urn II, the new composition of Urn II is 3 white balls and 7 black balls (since we added one ball from Urn I). The probability of picking a black ball from Urn II now is:

P(black ball from Urn II) = 7 / (3 + 7) = 7/10

(c) To calculate the probability that Urn I was chosen given that a black ball was picked, we can use Bayes' theorem. Let's denote event A as picking Urn I and event B as picking a black ball. We want to find P(A|B), which is the probability of picking Urn I given that a black ball was picked.

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

P(B|A) is the probability of picking a black ball given that Urn I was chosen. This is 4/7 since Urn I originally had 4 black balls out of 7 total balls.

P(A) is the probability of choosing Urn I initially, which is 2/3 since there are two urns and each is chosen with a probability of 1/2.

P(B) is the overall probability of picking a black ball, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

P(B|not A) is the probability of picking a black ball given that Urn II was chosen, which is 7/10.

P(not A) is the probability of not choosing Urn I initially, which is 1 - P(A) = 1 - 2/3 = 1/3.

Substituting these values into Bayes' theorem, we can find P(A|B).

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The integral test states that if a series is a sum of terms that are positive and decreasing, and if the terms of the series can be expressed as the values of a continuous and decreasing function, then the series converges if and only if the corresponding improper integral converges.

Let's apply the integral test to the given series. We need to find a continuous, positive, and decreasing function f(x) such that the series is the sum of the values of f(x) for x ranging from 2 to infinity.

For the first series, we have:

∑n=2∞n(lnn)p

Let f(x) = x(lnx)p. Then f(x) is continuous, positive, and decreasing for x ≥ 2. Moreover, we have:

f'(x) = (lnx)p + px(lnx)p-1

f''(x) = (lnx)p-1 + p(lnx)p-2 + p(lnx)p-1

Since f''(x) is positive for x ≥ 2 and p > 0, f(x) is concave up and the trapezoidal approximation underestimates the integral. Therefore, we have:

∫2∞f(x)dx = ∫2∞x(lnx)pdx

Using integration by substitution, let u = lnx, then du = 1/x dx. Therefore:

∫2∞x(lnx)pdx = ∫ln2∞u^pe^udu

Since the exponential function grows faster than any power of u, the integral converges if and only if p < -1.

For the second series, we have:

∑n=2∞1/n(ln⁡n)²

Let f(x) = 1/(x(lnx)²). Then f(x) is continuous, positive, and decreasing for x ≥ 2. Moreover, we have:

f'(x) = -(lnx-2)/(x(lnx)³)

f''(x) = (lnx-2)²/(x²(lnx)⁴) - 3(lnx-2)/(x²(lnx)⁴)

Since f''(x) is negative for x ≥ 2, f(x) is concave down and the trapezoidal approximation overestimates the integral. Therefore, we have:

∫2∞f(x)dx ≤ ∑n=2∞f(n) ≤ f(2) + ∫2∞f(x)dx

where the inequality follows from the fact that the series is the sum of the values of f(x) for x ranging from 2 to infinity.

Using the comparison test, we have:

∫2∞f(x)dx = ∫ln2∞(1/u²)du = 1/ln2

Therefore, the series converges if and only if p > 1.

In summary, the series ∑n=2∞n(lnn)p converges if and only if p < -1, and the series ∑n=2∞1/n(ln⁡n)² converges if and only if p > 1. For values of p such that -1 ≤ p ≤ 1, the series diverges.
To find the values of p for which the series converges or diverges using the integral test, we will first write the series and then perform the integral test.

The given series is:

∑(n=2 to infinity) [1/n(ln(n))^p]

Now, let's consider the function f(x) = 1/x(ln(x))^p for x ≥ 2. The function is continuous, positive, and decreasing for x ≥ 2 when p > 0.

We will now perform the integral test:

∫(2 to infinity) [1/x(ln(x))^p] dx

To evaluate this integral, we will use the substitution method:

Let u = ln(x), so du = (1/x) dx.

When x = 2, u = ln(2).
When x approaches infinity, u approaches infinity.

Now the integral becomes:

∫(ln(2) to infinity) [1/u^p] du

This is now an integral of the form ∫(a to infinity) [1/u^p] du, which converges when p > 1 and diverges when p ≤ 1.

So, for the given series:

- It converges when p > 1.
- It diverges when p ≤ 1.

In conclusion, using the integral test, the series ∑(n=2 to infinity) [1/n(ln(n))^p] converges for values of p > 1 and diverges for values of p ≤ 1.

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Answer:

4

Step-by-step explanation:

The amplitude of the sin graph is 4. Sin graphs are written as \(y=A sin(B(x-D))+C\) where A is the amplitude. In the equation above 4 is multiplied in front of sin, which shows it is the amplitude. Since 4 is the amplitude the graph will have a range of [-4,4].

Answer:

Hope ! answer helps you....

The purpose of Lend-Lease was to provide military aid to countries fighting against the Axis powers during set  World War II.

The purpose of Lend-Lease was to provide military aid to countries fighting against the Axis powers during World War II. The program was enacted by the United States in 1941 and allowed the US to provide war materials to its allies without requiring repayment. It was a major factor in the Allied victory, as it allowed the US to supply its allies with much needed war material and resources. The US provided a variety of goods, including food, oil, weapons, and tanks. It also supplied the Soviet Union with millions of tons of military equipment and supplies. Lend-Lease was instrumental in helping the Allies win the war, as it allowed them to gain a huge advantage over the Axis powers by providing essential supplies and resources.

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Answer:

D= 2z/p + 3/p = -z

Step-by-step explanation:

its C

Step-by-step explanation:

If there are 30 people and your 1 of them therefore it is C

The probability of your name being drawn first in a contest where there are 30 participants is 1 in 30.

To calculate the probability of your name being drawn first, we need to determine how many total outcomes there are and how many favorable outcomes there are. In this case, there are 30 people participating, and only one name is drawn first. So the total number of outcomes is 30, and the number of favorable outcomes is 1. To find the probability, divide the number of favorable outcomes by the total number of outcomes:

P(probability) = favorable outcomes / total outcomes

P = 1 / 30

The probability that your name will be drawn first is 1/30.

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Thus, the two factors of quadratic expressions found after factorization are 2 and 3.

Factorization is the technique of expressing a given statement as the product between two or more components. The sum of the greatest common factors of the integer coefficients and the same letters with the smallest powers yields the greatest common factor for two or more monomials.

Given quadratic expressions:

=  x² - 5x + 6

To factorize the expression, find the factors of 6 such that on addition it becomes -5.

= x² - 3x - 2x + 6

Taking x common from first two terms and -2 from last two terms.

= x(x -3) -2(x - 3)

Taking (x - 3) common.

= (x - 3)(x - 2)

x -3 = 0

x = 3

and, x - 2 = 0

x = 2

Thus, the two factors of quadratic expressions found after factorization are 2 and 3.

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Complete question:

Factorize quadratic expressions:  x² - 5x + 6

Step-by-step explanation:

Perhaps you entered your question incorrectly

maybe you meant

x^2 -x + 6     THIS factors to

(x-3)(x+2)     <=====if you multiply this out, you will see = x^2 -x+6

Are you familiar with the Quadratic Formula ?

   for this Quadrtatic     a = 1      b = -1      c = 6

    if you plug these numbers into the Quadratic Formula you get the roots:

            x = 3   and x = -2

       then you know the quadratic is   (x-3)(x+2)

Answer:

C. 1/2(18 x 6)

Step-by-step explanation:

1/2 base x height is the equation used, so plug in the numbers and you get 1/2(18 x 6)

Answer:

C

Step-by-step explanation:

We see that the shaded area of the rectangle is a right triangle. This is great for us.

The formula for finding the area of a triangle is (base*height)/2=area. Over here, the base is 18 and the height is 6, so we plug in those numbers and get (18*6)/2=108/2=54. I just went ahead and looked at all the answers knowing the answer but you can tell it isn't A or B because there is addition and you can tell it isn't A or C because it doesn't half it.

Please tell me if you have any questions.

Answer:

Height above the bottom gorge is 113 feet

Step-by-step explanation:

The width of the gorge = 40 feet

The height of the higher cliff = 158 feet

The height of the lower cliff = 98 feet

The length of the bridge = √((158-98)² + 40²) = 72.11 feet

The slope of the bridge = (158-98)/40 = 1.5

The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet

The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°

The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet

Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;

Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.

The 1930s was a period of significant change in the U.S. entertainment industry, with the emergence of new technologies and the development of new forms of media. Here are some of the key changes that took place:

Overall, the 1930s was a period of significant change in the U.S. entertainment industry, with the rise of new technologies and the emergence of new forms of media leading to the development of new genres and changing audience preferences.

Answer:

Mean, Median and Mode are collectively known as measures of central tendency

Step-by-step explanation:

They are used in statistics to represent and interpret data in various ways.