​$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%

Question 1

Question 2

Question 3

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.

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}

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 )

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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Answer:

hsjsjsjsjaiisisudujsjsjsjsj

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]

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]

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.

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

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]

Answer:

10

Step-by-step explanation:

10+3 = 13

13 x 7 = 91

Answer:

7(3x)=91

21x=91

x=91/21

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

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 =

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]

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.

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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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

Answer:

as the sample size increases, the margin of error decreases

Answer:

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.

Answer:

the answer is B

Step-by-step explanation:

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.

Answer:

33

1/2(83-50)=25

83-x=50

x=33

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

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

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.

Answer:

69

Step-by-step explanation:

xvusvsuvtuvqYSQY

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]

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.

Answer:

b. x^4 varies directly as y.

Step-by-step explanation:

x^4 = 7×y

x^4 is proportional to y.