$11,335
is invested, part at 9%
and the rest at 6%
. If the interest earned from the amount invested at 9%
exceeds the interest earned from the amount invested at 6%
by $865.35
, how much is invested at each rate? (Round to two decimal places if necessary.)

The equation that represents a proportional relationship

[tex]\[Y = \frac{1}{2}x\][/tex]

In a proportional relationship, the dependent variable (Y) is directly proportional to the independent variable (x). This means that as x increases or decreases, Y changes in a consistent ratio or fraction. In this equation, the ratio or fraction is [tex]\(\frac{1}{2}\)[/tex], indicating that for every unit increase in x, Y increases by [tex]\(\frac{1}{2}\)[/tex] units.

Let's break down the equation:

[tex]\(Y\)[/tex] represents the dependent variable, and it varies linearly with respect to the independent variable [tex]\(x\).[/tex]

The equation states that the value of Y is equal to [tex]\(\frac{1}{2}\)[/tex] times the value of [tex]\(x\).[/tex]

For example, if we have [tex]\(x = 4\)[/tex], we can substitute it into the equation to find the corresponding value of Y:

[tex]\[Y = \frac{1}{2}(4) = 2\][/tex]

So, when [tex]\(x\)[/tex] is 4, [tex]\(Y\)[/tex] is 2. This satisfies the proportional relationship because the ratio [tex]\(\frac{Y}{x}\)[/tex] remains constant at [tex]\(\frac{1}{2}\).[/tex]

Similarly, if we have [tex]\(x = -6\)[/tex], we can substitute it into the equation:

[tex]\[Y = \frac{1}{2}(-6) = -3\][/tex]

Therefore, when [tex]\(x\)[/tex] is -6, [tex]\(Y\)[/tex] is -3. Again, the ratio [tex]\(\frac{Y}{x}\)[/tex] remains constant at [tex]\(\frac{1}{2}\)[/tex].

Hence, the equation [tex]\(Y = \frac{1}{2}x\)[/tex] represents a proportional relationship where Y is directly proportional to x with a constant ratio of [tex]\(\frac{1}{2}\)[/tex].

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The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.

Note that the formula for finding the volume of a rectangular prism is given as:

Volume of rectangular prism = length * width * height.

Find the volume of each rectangular prism and add them together:

Volume of prism 1:

length = 10 m

width = 4 m

height = 3 m

Volume = 10 * 4 * 3 = 120 m³

Volume of prism 2:

length = 10 m

width = 1 m

height = 7 m

Volume = 10 * 1 * 7 = 70 m³

Total Volume = 120 + 70 = 190 m³.

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The correct test statistic for this hypothesis test is t = -2.88, not z = -2.65 or z = 2.65.

To perform a hypothesis test, we start by stating the alternative hypotheses:

H0: μ = 62 (the population temperature is 62 degrees F)

Ha: μ < 62 (the population  temperature is less than 62 degrees F)

X is the sample temperature, μ is the population temperature, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (59 - 62) / (6.21 / √(30)) = -2.88

Finally, we compare the test statistic to the critical value from the t-distribution with n - 1 f and an alpha level of 0.05. Since the alternative hypothesis is one-tailed (μ < 62), we use a one-tailed test and look up the critical value for a t-distribution with 29 f and an alpha level of 0.05. The critical value is -1.699.

Since the test statistic of -2.88 is smaller than the critical value of -1.699, we reject the null hypothesis and conclude that there is convincing evidence at the alpha = 0.05 level that the  temperature in fall and winter months in southwest is less than 62 degrees F.

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To find the volume of the figure, we use the formula: (2cm x 8cm x 7cm) + (1cm x 6cm x 8cm). The correct answer is (B)

To find the volume of a joined shape, you have to solve for the volume of each component of the shape and sum them together.

In this case, we have 2 shapes joined and both are cuboids.

Volume of a cuboid = length x breath x height

Volume₁ = 8 x 7 x 2 = 2 x 8 x 7

Volume₂ = 8 x 1 x 6 = 1 x 6 x 8

Total volume = (2cm x 8cm x 7cm) + (1cm x 6cm x 8cm)

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Okay, let's break this down step-by-step:

In the beginning of BS 2077, Dolma deposited B? 120,000 in her account.

The interest rate is 9% per annum.

So in the first year (BS 2077), she earned 9% of 120,000 = B? 10,800 in interest.

Her principal amount increased to 120,000 + 10,800 = B? 130,800

In BS 2078, she earned 9% of 130,800 = B? 11,772 in interest.

Her principal now was 130,800 + 11,772 = B? 142,572

In BS 2079, she earned 9% of 142,572 = B? 12,781 in interest.

Her principal now was 142,572 + 12,781 = B? 155,353

In the beginning of BS 2080, her total balance was B? 155,353.

She paid 6% of her interest as income tax.

9% of 155,353 is 13,991.

6% of 13,991 is 839.

So her total interest received in BS 2080 after paying tax was 13,991 - 839 = B? 13,152.

Her total amount received in BS 2080 was:

Principal (155,353) + Interest (13,152) = B? 168,505

So the total amount Dolma received in the beginning of BS 2080 was B? 168,505

Let me know if you have any other questions!

Answer: 11x16x5=880

This means the answer is C

Based on the image attached, The the shape of the distribution is option c) data skewed right.

The term Right skewed is one where the mean  is more prominent than the middle. The mean overestimates the foremost common values in a emphatically skewed dispersion. Cleared out skewed: The mean is less than the median. The mean  is one that has little of the common values in a rightly skewed dissemination.

So, therefore, if  most of the information are on the cleared out side of the histogram but many larger values are on the proper, the information are said to be skewed to the right.

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See text below



Gabriela recorded the ages of her shirts.

·

0 1 2 3 4 5 6 7 8 9 10

Age (years)

Which of these best describes the shape of the distribution?

Choose 1 answer:

Roughly symmetric

Skewed left

Skewed right

Good Question (141)

Answer:

x = 8.8 cm

Step-by-step explanation:

This is a right-angled triangle, and we are given two sides, so we can use pythagoras Theoren

[tex]a^{2} +b^{2} =c^{2}[/tex]

Where 'c' is the hypotenuse (the longest side in right angled triangle and is always opposite to the 90 degree angle).

'a' and 'b' are the other two sides.

So now we have:

2.6^2 + x^2 = 9.2^2 (Solve for 'x')

x^2 = 9.2^2 - 2.6^2

x = [tex]\sqrt{9.2^{2} - 2.6^{2} }[/tex]

x = 8.8 cm (2 s.f. as other dimensions are also 2 s.f.)

After considering all the given data we conclude that the measure of m∠E is 54.46° under the condition that ADEF is a right angled triangle.

We already know that ADEF is a right angled triangle having sides EF = 6 and FD = 4, we can apply the Pythagorean theorem to evaluate the length of the hypotenuse AD.
AD = √(6² + 4²)
= √52)
≈ 7.21
Now we can apply the sine function to find the measure of angle E.
sin(E) = opposite/hypotenuse = EF/AD
E = arcsin(EF/AD)
≈ 54.46°
Therefore,  m∠E  ≈ 54.46°.
The Pythagorean Theorem is considered a fundamental relation in the context of Euclidean geometry comparing the three sides of a right triangle.
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Answer: 678

Step-by-step explanation: ii

The statement, "You can prove two triangles are similar using an AA similarity theorem" is true while the statement "If the side length of similar figures have a ratio of m/n then the volume will have a ratio of n m³/n³. The correct ratio is (m/n)³" is false.

Visual Match is a term used to describe the degree of similarity or resemblance between two visual elements or objects.

From the given question, we can arrange the following statements as below:

TRUE

- You can prove two triangles are similar using an AA similarity theorem.

- If the side length of similar figures have a ratio of m/n then the surface area will have a ratio of (m/n)².

- If the side length of similar figures have a ratio of m/n then the area will have a ratio of (m/n)².

FALSE

- If the side length of similar figures have a ratio of m/n then the volume will have a ratio of n m³/n³. The correct ratio is (m/n)³.

- If the side length of similar figures have a ratio of 2/3 then the perimeter will have a ratio of 2/3. The correct ratio is 2/3.

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To measure the length of the segment, place a ruler measured in centimeters on the surface and record the length of choice.

If you want to determine any line segment, use a ruler that is calibrated in centimeters (as is the case in the above), inches, or meters. Place the ruler on the paper or drawing platform and draw a line that matches the corresponding figure.

If the measure of the line segment is 8.3 cm then trace that length on the surface. To bisect the line segment, draw a vertical line across the horizontal one and divide the opposite sides by 2.

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Answer: 5, 9

Step-by-step explanation:

factors of 45:

1, 3, 5, 9, 15, 45

Sums: 46, 24, 14

the factors 5 and 9 multiply to get 45 and add to get 14

voila!

Answer:

64 - (6 x 8)

Step-by-step explanation:

"The product of 6 and 8" means 6 and 8 multiplied together, therefore this part can be expressed as 6x8. "Subtracted from 64" means that the product of 6x8 is being taken away from 64, therefore it is 64-(6x8).

Answer:

A. Point estimates are used to make inferences about population parameters.

[tex]|\Omega|=6^2=36\\A=\{(1,1),(1,4),(4,1),(2,3),(3,2)\}\\|A|=5\\\\P(A)=\dfrac{5}{36}\approx13.9\%[/tex]

answer

(z+2)(z-2)

steps

its a rule

a²-b²= (a+b) (a-b)

vedantu

The probability that we will get a lead role, given that we are chosen to be in the play is 0.7.

We have,

Probability is the ratio that shows the likelihood of an event occurring from a given set of possible events.

We can find the required probability below:

The probability that we will be chosen for the play is 0.5.

The probability that we will get the lead role is 0.2.

In this situation, the probability can be found by adding the probability of being chosen and the probability that we will get the lead role.

The probability that we get a lead role, = The probability that we will be chosen for the play + The probability that we will get the lead role

= 0.5 + 0.2

= 0.7

The probability of us getting a lead role given that we have already been chosen for the play is found to be 0.7. The correct answer is option C.

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complete question:

You are trying out for the school play. The probability that you are chosen to

be in the play is 0.5. The probability that you get a lead role is 0.2. What is the

probability that you get a lead role, given that you are chosen to be in the

play?

O A. 0.5

Oo oo

O B. 0.4

O c. o7

O D.0.3​

The area of the regular polygon, given the apothem and the side length, would be 52. 5 in².

To find the area of a regular pentagon with a given apothem (a) and side length (s), we can use the formula:

Area = ( Perimeter × Apothem ) / 2

Perimeter would be :

= 5 x sides

= 5 x 6

= 30 inch

The area is therefore :

= ( Perimeter × Apothem ) / 2

= ( 30 in x 3. 5 in ) / 2

= 105 / 2

= 52. 5 in²

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The maximum amount Lauren should budget for housing is $445.50 per month.

Now, A good rule of thumb is that housing expenses should not exceed 30% of her income.

So, We get;

30% of Lauren's monthly income of $1485 would be:

= 30% x $1485

= $445.50

Therefore, the maximum amount Lauren should budget for housing is $445.50 per month.

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Answer:

Let x be the cost of the pass.

Then the cost of the souvenir is (2/3)x.

The cost of the burger is (1/4) of the cost of the souvenir, which is (1/4)(2/3)x = (1/6)x.

The total cost of the items is x + (2/3)x + (1/6)x = (11/6)x.

Tim had $2.00 left over after buying these items, so we can set up the equation:

(11/6)x + 2 = 40.50

Solving for x, we get:

x = 18

Therefore, the cost of the pass is $18, the cost of the souvenir is (2/3)($18) = $12, and the cost of the burger is (1/6)($18) = $3.

Answer:

5 (19 + 12)

Step-by-step explanation:

You add up the red and black pens and multiply by 5, which indicates the 5 bags

Answer:

OD) x = -2, -5

Step-by-step explanation:

To solve the quadratic equation x^2 + 7x + 10 = 0, we can use factoring or the quadratic formula.

Using factoring:

We need to find two numbers whose sum is 7 and whose product is 10. These numbers are 2 and 5. So, we can write x^2 + 7x + 10 = 0 as (x + 2)(x + 5) = 0.

Setting each factor to 0, we get x + 2 = 0 or x + 5 = 0. Solving for x, we get x = -2 or x = -5.

Using the quadratic formula:

The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 7, and c = 10.

Substituting these values into the formula, we get x = (-7 ± sqrt(7^2 - 4(1)(10))) / 2(1)

Simplifying, we get x = (-7 ± sqrt(9)) / 2

Therefore, x = (-7 + 3) / 2 or x = (-7 - 3) / 2

Solving for x, we get x = -2 or x = -5.

Thus, the solutions of the quadratic equation x^2 + 7x + 10 = 0 are x = -2 or x = -5.

Therefore, the answer is (OD) x = -2, -5.

The area of the figure will be 17 square centimeters.

The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the figure is the summation of the area of the two rectangles. Then the area of the figure is calculated as,

A = 3 x 5 + 1 x 2

A = 15 + 2

A = 17 square cm

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1) Note that the population mean is 153.

2) there are 36 possible random samples of size two that can be selected from a population of nine.

1) Population Mean = (172 + 148 + 156 + 170 + 161 + 138 + 142 + 156 + 134) / 9

= 1377 / 9

Population Mean = 153

2) To get the number of possible random samples, we must use Combination whose equation is given as

nCr = n! / (r! (n-r)!)

nC2 = 9! / (2!(9-2)!)

= 9! / (2! 7!)

= (9 x 8 x 7!) / (2!7!)

= (9 x 8) / 2

= 36

Thus, the number of random samples that can be selected form a population of 9 is 36.

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The height of the square pyramid is approximately 91.92 inches.

In a square pyramid, the slant height (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height (s). We can express this relationship as:

[tex]s^2 = (b/2)^2 + h^2[/tex]

Given that the length of one side of the base (b) is 25.2 in and the slant height (s) is 93.7 in, we can substitute these values into the equation:

[tex]93.7^2 = (25.2/2)^2 + h^2[/tex]

Simplifying:

[tex]8761.69 = 316.8 + h^2[/tex]

Subtracting 316.8 from both sides:

[tex]h^2 = 8444.89[/tex]

Taking the square root of both sides:

h ≈ 91.92 in

Therefore, the height of the square pyramid is approximately 91.92 inches.

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The cost of electricity consumption (excluding VAT) for a household using 196 kWh in a month is given by [tex]\( \text{Cost} = 196 \, \text{kWh} \times r \), where \( r \)[/tex]represents the rate per kilowatt-hour charged by the electricity provider.

To determine the cost of electricity consumption excluding VAT, we need to know the rate charged per kilowatt-hour (kWh) by the electricity provider. Let's denote this rate as [tex]\(r\)[/tex] (in currency per kWh).

The total cost of electricity consumption (excluding VAT) can be calculated by multiplying the electricity usage in kWh by the rate:

[tex]\[ \text{Cost} = \text{Usage} \times \text{Rate} \][/tex]

Given that the household uses 196 kWh in a month, the cost can be expressed as:

[tex]\[ \text{Cost} = 196 \, \text{kWh} \times r \][/tex]

Please note that we still need the specific rate per kWh from the electricity provider to calculate the actual cost.

The cost of electricity consumption (excluding VAT) for a household using 196 kWh in a month is given by [tex]\( \text{Cost} = 196 \, \text{kWh} \times r \), where \( r \)[/tex]represents the rate per kilowatt-hour charged by the electricity provider.

Note: The given question is incomplete. The complete question is:

If a household uses 196kWh of electricity in a month how much would they pay for their electricity consumption excluding VAT?

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