​$6300 is​ invested, part of it at 11​% and part of it at 6​%. For a certain​ year, the total yield is ​$533.00. How much was invested at each​ rate?
$___ was invested at 11%

Answers

Answer 1

Answer:

Invested at 11% : 3100

Invested at 6% : 3200

Step-by-step explanation:

let x= amount invested at 11%

let y= amount invested at 6%

we can write

Equation 1: x+y=6300

Equation2: .11x+.06y=533

Divide equation 2 by .06 to get

1.8333333x+y=8883.33333333

Subtract equation 2 from equation 1

.8333333x= 2583.33333333

x= 3100

Plug in x= 3100 into equation 1

3100+y= 6300

y= 3200


Related Questions



If x + y =6, y +z = 7 and z + x =9, what is the average (arithmetic mean) of
x,y and z?

Answers

Answer:

[tex]\frac{22}{3}[/tex]

Step-by-step explanation:

x + y + y + z + z + x = 2x + 2y + 2z = 22

x + y + z = 22

22 ÷ 3 = [tex]\frac{22}{3}[/tex]

Kern Shipping Inc. has a requirement that all packages must be such that the combined length plus the girth (the perimeter of the cross section) cannot exceed 99 inches. Your goal is to find the package of maximum volume that can be sent by Kern Shipping. Assume that the base is a square.

a. Write the restriction and objective formulas in terms of x and y. Clearly label each.
b. Use the two formulas from part (a) to write volume as a function of x, V(x). Show all steps.

Answers

Answer:

Step-by-step explanation:

From the given information:

a)

Assuming the shape of the base is square,

suppose the base of each side = x

Then the perimeter of the base of the square = 4x

Suppose the length of the package from the base = y; &

the height is also = x

Now, the restriction formula can be computed as:

y + 4x ≤ 99

The objective function:

i.e maximize volume V = l × b × h

V = (y)*(x)*(x)

V = x²y

b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):

y + 4x ≤ 99   --- (1)

V = x²y          --- (2)

From equation (1),

y ≤ 99 - 4x

replace the value of y into (2)

V ≤ x² (99-4x)

V ≤ 99x² - 4x³

Maximum value V = 99x² - 4x³

At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]

[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]

⇒ 198x - 12x² = 0

[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]

By solving for x:

x = 0 or x = [tex]\dfrac{33}{2}[/tex]

Again:

V = 99x² - 4x³

[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]

At x = [tex]\dfrac{33}{2}[/tex]

[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]

[tex]\implies 198 - 12 \times 33[/tex]

= -198

Thus, at maximum value;

[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]

Recall y = 99 - 4x

when at maximum x = [tex]\dfrac{33}{2}[/tex]

[tex]y = 99 - 4(\dfrac{33}{2})[/tex]

y = 33

Finally; the volume V = x² y is;

[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]

[tex]V =272.25 \times 33[/tex]

V = 8984.25 inches³

7056 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows and the number of plants in each row​

Answers

Answer:

84 rows

84 plants on each row

Step-by-step explanation:

Given

[tex]Plants = 7056[/tex]

Required

The number of rows

Since the number of rows (r) and the plants on each row (p) are the same, then the area to be planted on is:

[tex]Plants = r * p[/tex]

Where

[tex]r =p[/tex]

So, we have:

[tex]Plants = r * r[/tex]

[tex]Plants = r^2[/tex]

This gives:

[tex]7056 = r^2[/tex]

Take square roots

[tex]84 = r[/tex]

Rewrite

[tex]r = 84[/tex]

What is the volume of the cylinder below?
3

Answers

You need to add a picture
I can help but please show us a picture

A science teacher wrote the table of values below.
Amount of Hydrogen vs. pH
pH, f(x)
Amount of Hydrogen, X
(in moles per liter)
1
10
1
2
1
100
3
3
1
1,000
4
1
10.000
-
5
1
100,000
Which function models the data in the table?

Answers

Answer:

B

Step-by-step explanation:

Took quiz

The logarithmic function for the teacher who wrote the table of values with amount of hydrogen and pH level is given by f ( x ) = log ( 1/x )

What is Logarithm?

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the function be represented as f ( x )

Now , the values of x are

x = { 1/10 , 1/100 , 1/1000 , 1/10000 , 1/100000 }

where x represents the amount of Hydrogen in moles per liter

And the values of f ( x ) = { 1 , 2 , 3 , 4 , 5 }

where y represents the pH level

So , when x = 1/10 , f ( x ) = 1

And , the logarithmic equation is given as

f ( x ) = log ( 1/x )

when x = 1/1000

f ( 1/1000 ) = log ( 1/1/1000 )

f ( 1/1000 ) = log ( 1000 )

f ( 1/1000 ) = 3

Therefore , the value of f ( x ) is log ( 1/x )

Hence , the logarithmic equation is f ( x ) = log ( 1/x )

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What is the relation between the variables in the equation
X^4/y=7?

a. x varies inversely as y
b. x4 varies directly as y
c. y varies directly as x4
d. y varies inversely as x4

Answers

Answer:

b. x^4 varies directly as y.

Step-by-step explanation:

x^4 = 7×y

x^4 is proportional to y.

Help?!??? What is the distance!
Trig. Ch.7.1

Answers

9514 1404 393

Answer:

  100 m

Step-by-step explanation:

One side between two angles is given, so we need to find the third angle. The sum of angles in a triangle is 180°, so the third angle is ...

  A = 180° -110°20' -13°20' = 56°20'

The law of sines can be used to find the length of side AB:

  AB/sin(C) = BC/sin(A)

  AB = BC·sin(C)/sin(A) . . . . multiply by sin(C)

  AB = (360 m)sin(13°20')/sin(56°20') ≈ 99.75253 m

The distance AB across the river is about 100 m.

A populations instantaneous growth rate is the rate at which it grows for every instant in time. Function r gives the instantaneous growth rate of a bacterial culture x hours after the start of an experiment How many hours after the experiment began was the instantaneous growth rate equal to 0? r(x)=0.01(x+2)(x^2 -9) A. 9 B. 2 C. 0 D. 3

Answers

Answer:

3

Step-by-step explanation:

r(x) = 0.01(x + 2)(x^2 - 9)

We are looking fo the value of x at which r(x) = 0.

We set the function equal to 0 and solve for x.

0.01(x + 2)(x^2 - 9) = 0

Divide both sides by 0.01. Factor x^2 - 9 as the difference of two squares.

(x + 2)(x + 3)(x - 3) = 0

x + 2 = 0  or  x + 3 = 0  or x - 3 = 0

x = -2  or x = -3  or x = 3

Since we are looking for a time after the experiment started, and it started at x = 0, we discard the negative answers, and we keep x = 3.

Answer: 3

Answer:

3

Step-by-step explanation:

EDMENTUM

Abigail is using blocks to build a tower. The blocks are 3 inches, 4 inches, and 8 inches tall. She has stack 3 blocks. How many different heights are possible for the tower?

Answers

9514 1404 393

Answer:

  10

Step-by-step explanation:

Possible tower heights using 3 blocks are ...

  {9, 10, 11, 12, 14, 15, 16, 19, 20, 24}

There are 10 different heights possible.

_____

Each block can be used 1, 2, or 3 times.

Using a 3 in block as the smallest, we have ...

  3+3+3 = 9

  3+3+4 = 10

  3+3+8 = 14

  3+4+4 = 11

  3+4+8 = 15

  3+8+8 = 19

Using a 4-in block as the smallest, we have ...

  4+4+4 =12

  4+4+8 = 16

  4+8+8 = 20

And ...

  8+8+8 = 24

What sample size is needed to give a margin of error within in estimating a population mean with 95% confidence, assuming a previous sample had .

Answers

Answer:

[tex]n = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]

The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion [tex]\pi[/tex](if no previous estimate use 0.5) and M is the desired margin of error.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Needed sample size:

The needed sample size is n. We have that:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]\sqrt{n}M = 1.96\sqrt{\pi(1-\pi)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{\pi(1-\pi)}}{M}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]

[tex]n = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]

The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion [tex]\pi[/tex](if no previous estimate use 0.5) and M is the desired margin of error.

If you answer this you will get 100 points pls answer hurry it’s due in 20 mins

Answers

Ye the answer is 1...

Answer:

Option B, median

Step-by-step explanation:

We see the data is not uniform. One of the prices is very high compared to the others. Since there is an outlier, the median is the best measure of central tendency.

This is the second option.

two thirds of a number is negative six. find the number

Answers

Answer:

-9

Step-by-step explanation:

Two-thirds of a number is negative six. The number is -9. Let the number is x, 2/3x =-6, x=-6x3/2=-9.

If 3 is added to a number and the sum is multiplied by 7,gives 91 as result. Find the number.​

Answers

Answer:

10

Step-by-step explanation:

10+3 = 13

13 x 7 = 91

Answer:

7(3x)=91

21x=91

x=91/21

The parent function f(x) 3 to the square root of x is transformed to g(x)=2f(x-3). Which is the graph of g(x)?

Answers

Because of this. The answer is B

Answer:

the answer is B

Step-by-step explanation:

HELP!!!

A spherical baseball has a diameter of 5 inches and weighs 7 grams per cubic inch. What is the closest weight of the baseball rounded to the nearest gram?

Answers

Answer:

69

Step-by-step explanation:

xvusvsuvtuvqYSQY

If A = {x x is an even integer), B = {xx is an odd integer), C = {2, 3, 4, 5), and D = {8, 9, 10, 11), list the element(s) of the following set.
AND
An D= { } (Use a comma to separate elements in the set.)

Answers

Answer:

AnD = {8,10}

Step-by-step explanation:

A = {2, 4, 6, 8 ,10 ...}

B = {1, 3, 5, 7 ,9 ...}

C = {,2 ,3 ,4 ,5 ...}

D = { 8, 9 ,10 ,11 ...}

AnD = {8, 10}

plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help me i really do need the help

Each of the problems below was solved incorrectly, for each problem, find the mistake in the work/ answer. Explain what the mistake is, and find the correct answer.


Explain the mistake:








Find the correct answer(equation):




2. Find the value of x

Explain the mistake:









Find the correct answer(equation):


3. Find the value of x

Explain the mistake:









Find the correct answer(equation):

Answers

Question 1

The mistake is that vertical angles are congruent, and don't always add up to 180 degrees.[tex]5x=100 \longrightarrow x=20[/tex]

Question 2

Angles that add to form a right angle add to 90 degrees, not 180 degrees.[tex]3x+39=90 \longrightarrow 3x=51 \longrightarrow x=17[/tex]

Question 3

Angles that add to form a right angle add to 90 degrees, not 180 degrees.[tex]3x+39=90 \longrightarrow 3x=51 \longrightarrow x=17[/tex]

Solve one-sixth ÷ 6 = ___

Answers

Answer:6/6

Step-by-step explanation:

1/6 divide 6

Keep

Flip

Change

your gonna keep 1/6 as a fraction

then flip the second fraction so 6 would’ve been 6/1 but it’s gonna flip so it should look like this 1/6

after you will change the  sign so the division will become multipliaction so it should look like 1/6 x 6/1 which will equal to 6/6

Names the figures in two different ways.

Answers

Answer:

hsjsjsjsjaiisisudujsjsjsjsj

Person A leaves his home to visit his​ cousin, person​ B, who lives 243 miles away. He travels at an average rate of 46 miles per hour. One​ half-hour later, person B leaves her house to visit person​ A, traveling at an average rate of 64 miles per hour. How long after person B leaves will it be before they​ meet?

Answers

They meet (or pass) each other two hours after B leaves.

When B starts trip A has already gone 23 miles (46 x 0.5)
This means they are still 220 miles apart.
Their closing speed is 46 + 64 = 110 mph.
They will meet 2 hours after B leaves home. (220 / 110)

A will have travelled 46 x 2.5 = 115 miles and B will have travelled 2 x 64 = 128 miles

Sue believes that the two cylinders shown in the diagram have equal volumes. Is Sue correct? Explain why or why not

Answers

Sue is correct because the two cylinders have the same base area and the same height.

Sui believes that the two cylinders have an equal volume is correct.

The volume of cylinder = Base area×Height

=(πr²)×(height)

This is also true for oblique cylinder.

Both cylinders have same height and radius also so, both cylinders have equal volume.

V=πr²h

V=π×(5)²×11.5

V=903.208m³

It can also be visualized that the oblique cylinder have circular pieces. These pieces can be solid together to form a regular cylinder with the same height (i.e. 11.4 m). So both the cylinders have equal volume.

What is a cylinder?

A cylinder is a three-dimensional shape in geometry. A cylinder is round and has a top and bottom in the shape of a circle. The top and bottom are flat and always the same size.

Thus, Sue is correct, and it's true that the two cylinders shown in the diagram have equal volumes.

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Round 3,872.3155 to the nearest hundred

Answers

Answer:

3,872.316

Step-by-step explanation:

Answer:

to nearest hundreds it would be: 3,900

Step-by-step explanation:

872 it closer to 900 than 800

Identify the relationship between sampling error and sample size.

Answers

Answer:

as the sample size increases, the margin of error decreases

find the smallest number by which 2925 should be divided to be a perfect square​

Answers

Answer: 13

Step-by-step explanation:

Given

The number is 2925

The prime factorization of 2925 is

[tex]\Rightarrow 2925=3\times 3\times 5\times 5\times 13\\\Rightarrow 2925=3^2\times 5^2\times 13[/tex]

To make 2925 a perfect square, we have to eliminate 13 from it, so divide 2925 by 13 to make it a perfect square

The perfect Sqaure becomes [tex](3\times 5)^2=225[/tex]

Consider the following confidence interval interpretation: We are 98% confident that the true mean laptop screen size is between 19.2 and 21.4 inches. Is this interpretation of a confidence interval correct or incorrect

Answers

Answer:

Incorrect

Step-by-step explanation:

This interpretation is incorrect because it states that 98% of the data is with in the confidence interval.

or 98% of the laptop have screen size between 19.2 and 21.4 inches

However, the interpretation would have been correct if it would have stated as - Value of the population mean i.e mean size of the laptop screen lies within the confidence interval.

How many 1/6 cup serving of rice and in 2/3 cup of rice

Answers

Answer:

4 serving cups

Step-by-step explanation:

Given

[tex]Serving\ cup = \frac{1}{6}[/tex]

[tex]Rice\ cup = \frac{2}{3}[/tex]

Required

The number of serving cup (n)

This is calculated by dividing the rice cup by the serving cup

[tex]n = \frac{Rice\ cup}{Serving\ cup}[/tex]

[tex]n = \frac{2/3}{1/6}[/tex]

Rewrite as:

[tex]n = \frac{2}{3} \div \frac{1}{6}[/tex]

Change to multiplication

[tex]n = \frac{2}{3} * \frac{6}{1}[/tex]

[tex]n = \frac{12}{3}[/tex]

[tex]n=4[/tex]

can someone answer this please

Answers

Area is trapezium =
A=1/2h(a+b)

84=1/2(6)(7+b)

84=3(7+b)

84=21+3b

3b=84-21

B=63/3

B= 21 cm

I’m sorry if my answer turned out to be wrong but I tried my best so best of luck !!

Answer:

x = 14

Step-by-step explanation:

Please note, the word trapezium is a synonym for the word trapezoid.

This problem gives one the area of the trapezoid, a well as one of the measurements of a base and the height of the figure. One is asked to find the length of the other base. This can be done by using the formula to find the area of a trapezoid. This formula is the following,

[tex]A=(h)(\frac{b_1+b_2}{2})[/tex]

Where (A) represents the area of a trapezoid, ([tex]b_1[/tex]) and ([tex]b_2[/tex]) represents the bases and (h) represents the height. Substitute in the given values and solve for the unknown base.

[tex]b_1=7\\h=6\\A=84[/tex]

[tex]A=(h)(\frac{b_1+b_2}{2})\\[/tex]

Substitute,

[tex]84=6(\frac{7+b_2}{2})\\[/tex]

Inverse operations,

[tex]84=6(\frac{7+b_2}{2})[/tex]

[tex]14=\frac{7+b_2}{2}[/tex]

[tex]28=7+b_2[/tex]

[tex]14=b_2[/tex]

Help me pls and thanks important!!!!

Answers

Answer:

33

1/2(83-50)=25

83-x=50

x=33

The hypotenuse of a right triangle is 13 ft long. The longer leg is 7 ft longer than the shorter leg. Find the side lengths of the triangle.

Answers

Answer:

The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.

Step-by-step explanation:

Let the shorter leg be x.

Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (x + 7).

Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by:

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

Where a and b are the side lengths and c is the hypotenuse.

The hypotenuse is 13 and the legs are x and (x + 7). Substitute:

[tex](x)^2+(x+7)^2=(13)^2[/tex]

Square:

[tex]x^2+x^2+14x+49=169[/tex]

Simplify:

[tex]2x^2+14x-120=0[/tex]

We can divide both sides by two:

[tex]x^2+7x-60=0[/tex]

Factor:

[tex](x-5)(x+12)=0[/tex]

Zero Product Property:

[tex]x-5=0\text{ or }x+12=0[/tex]

Solve for each case:

[tex]x=5\text{ or } x=-12[/tex]

Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is:

[tex]x=5[/tex]

The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.

Which sentence describes a way to determine the missing number number in the pattern?

Answers

Answer:

70910 not sure

Step-by-step explanation:

70.91 x 10 = 709.1 70.91 x 100 = 7,091 70.91 x 1,000 =

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