A bank loaned out ​$20,000​, part of it at the rate of 6 % per year and the rest at 16 % per year. If the interest received in one year totaled ​$1500​, how much was loaned at 6 %?

Answer: a) additive inverse (addition)

              b) multiplicative inverse (division)

Step-by-step explanation:

Step 2: 6 is being added to both sides

Step 4: (3/4) is being divided from both sides

It is difficult to know what options are provided in the drop-down menu without seeing them. If I was to complete a proof and justify each step, then the following justifications would be used:

Step 2: Addition Property of Equality

Step 4: Division Property of Equality

Slope is the change in y over the change in x

Slope = (1-0) /( -3 - -4)

Slope = 1/1

Slope = 1

Hey there! I'm happy to help!

We see that if the river isn't moving at all the boat can move at 18 mph (most likely because it has an engine propelling it.)

We want to set up a proportion where our 21 miles downstream time is equal to our 15 miles upstream time so we can find the speed. A proportion is basically showing that two ratios are equal. Since our downstream distance and upstream distance can be done in the same amount of time, we will write it as a proportion.

We want to find the speed of the river. We will use r to represent the speed of the river. When going downstream, the boat will go faster, so it will have a higher mph. So, our speed going down is 18+r. When you are going upstream, it's the opposite, so it will be 18-r.

[tex]\frac{distance}{speed} =\frac{21}{18+r} = \frac{15}{18-r}[/tex]

So, how do we figure out what r is now? Well, one nice thing to know about proportions is that the product of the items diagonal from each other equals the product of the other items. Basically, that means that 15(18+r) is equal to 21(18-r). This is a very nice trick to solve proportions quickly. We see that we have made an equation and now we can solve it!

15(18+r)=21(18-r)

We use the distributive property to undo the parentheses.

270+15r=378-21r

We subtract 270 from both sides.

15r=108-21

We add 21 to both sides.

36r=108

We divide both sides by 36.

r=3

Therefore, the speed of the river is 3 mph.

You also could have noticed that 18mph to 21 mph is +3, and 18mph to 15 mph -3 in -3 mph, so the speed of the river is 3 mph. That would have been a quicker way to solve it XD!

Have a wonderful day!

Answer:

The  probability of a bulb lasting for at most 552 hours.

P(x>552)  = 0.0515

Step-by-step explanation:

Step(i):-

Given mean of the life time of a bulb = 510 hours

Standard deviation of the lifetime of a bulb = 25 hours

Let 'X' be the random variable in normal distribution

Let 'x' = 552

[tex]Z = \frac{x-mean}{S.D} = \frac{552-510}{25} =1.628[/tex]

Step(ii):-

The  probability of a bulb lasting for at most 552 hours.

P(x>552) = P(Z>1.63)

               = 1- P( Z< 1.63)

               =  1 - ( 0.5 + A(1.63)

              =   1- 0.5 - A(1.63)

              =   0.5 -A(1.63)

              =   0.5 -0.4485

             =  0.0515

Conclusion:-

The  probability of a bulb lasting for at most 552 hours.

P(x>552)  = 0.0515

Answer:

Step-by-step explanation:

[tex]x + 3 = 6[/tex]

Move constant to R.H.S and change its sign:

[tex]x = 6 - 3[/tex]

Calculate the difference

[tex]x = 3[/tex]

Hope this helps...

Good luck on your assignment..

If [tex]f(x)=\mid x\mid[/tex] and [tex]g(x)=x+2[/tex] then [tex]f(g(x))=\mid x+2\mid[/tex].

The domain is [tex]x\in(-\infty, +\infty)=\mathbb{R}[/tex].

The range is [tex]y\in[2,+\infty)[/tex].

Hope this helps.

Answer:

Step-by-step explanation:

with range there is a horizontal line under the > sign, just as a side note:D

BRANLIEST?

Answer:

Jill bought 16 books and Sam bought 9 books

Step-by-step explanation:

Let the number of books that Jill bought be j.

Let the number of books that Sam bought be s.

Jill bought 7 more books than Sam:

j = 7 + s

They bought 25 books altogether:

j + s = 25

Put j = 7 + s into the second equation:

7 + s + s = 25

7 + 2s = 25

2s = 25 - 7 = 18

s = 18/2 = 9 books

Therefore:

j = 7 + s = 7 + 9

s = 16 books

Jill bought 16 books and Sam bought 9 books.

Answer:

A. f(x) = x^2 + 4x + 3

D. f(x) = -2x^2 - 8x + 1

Step-by-step explanation:

The axis of symmetry is found by h = -b/2a  where ax^2 +bx +c

A. f(x) = x^2 + 4x + 3

  h = -4/2*1 = -2    x=-2

B. f(x) = x^2 - 4x - 5

h = - -4/2*1 = 4/2 =2  x=2  not -2

C. f(x) = x^2 + 6x + 2

h =  -6/2*1 = -3/2 =  x=-3/2  not -2

D. f(x) = -2x^2 - 8x + 1

h = - -8/2*-2 = 8/-4 =-2  x=-2  

E. f(x) = -2x^2 + 8x - 2

h = - 8/2*-2 = -8/-4 =2  x=2  not -2

Answer:

Hey there! The answer to this question is

A. f(x) = x^2 + 4x + 3

D. f(x) = -2x^2 - 8x + 1

Answer:

x  =  8   ( 20$ bills)

y  = 5    ( 10 $ bills)

z = 2     ( 5  $  bills)

Step-by-step explanation:

Let call x, y, and z the number of bill of 20, 10, and 5 $ respectively

then according to problem statement, we can write

20*x + 10*y + 5*z = 220         (1)

We also know the total number of bills (15), then

x + y + z = 15     (2)

And that quantity of 20 $ bill is equal to

x = 3 + y     (3)

Now we got a three equation system we have to solve for x, y, and z for which we can use any valid procedure.

As    x = 3 + y    by substitution in equation (2)   and (1)

( 3 + y ) + y + z  = 15       ⇒   3 + 2*y + z = 15  ⇒  2*y + z = 12

20* ( 3 + y ) + 10*y + 5*z  = 220  ⇒ 60 + 20*y + 10*y + 5*z = 220

30*y + 5*z  = 160      (a)

Now we have only 2 equations

2*y + z = 12   ⇒    z = 12 - 2*y

30*y + 5*z  = 160     30*y  + 5* ( 12 - 2*y) = 160

30*y  + 60 - 10*y = 160

20*y = 100

y = 100/20       y = 5      Then by substitution in (a)

30*y + 5*z = 160

30*5  + 5*z = 160

150 + 5*z  = 160    ⇒     5*z = 10     z = 10/5      z = 2

And x

x + y + z = 15

x + 5 + 2 = 15

x = 8

Answer:

x=8 y=5 x=2

Step-by-step explanation:

Answer:

First choice

Step-by-step explanation:

Start by arranging the exponents of 10 in ascending order.

9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7 * 10^3

The exponents are in ascending order, -8, -6, 3, 3

Since the last two exponents are equal, we must compare the numbers that multiply the powers of 10. They are 2.5 and 7. Since 2.5 < 7, ascending order is 2.5, 7. That means the line above is in ascending order.

Answer: First choice

Answer:

D) 86 – 18x – 8 = 12x + 18

X = 2

Step-by-step explanation:

86 – 2 (9x + 4) = 12x + 18

This question has a straight forward answer...

It's just to open up the bracket and ensure that the negative sign before the bracket multiply the values in the bracket exactly.

So opening up the bracket gives us this as the answer

86 - 18x -8 = 12x +18

86-18-8 = 12x+ 18x

60 = 30x

X = 2

Answer:

I noticed a pattern:

3 * 2 + 6 = 12 and 2 * 2 + 5 = 9

This means that a*b = 2a + b.

Answer:

c=21

Step-by-step explanation:

[tex]3(c-5)=48\\3c-15=48\\3c=48+15\\3c=63\\c=63/3\\c=21[/tex]

Hope this helps,

plx give brainliest

Answer:

c=21

Step-by-step explanation:

3(c−5)=48

Divide both sides by 3.

c-5=48/3

Divide 48 by 3 to get 16.

c−5=16

Add 5 to both sides.

c=16+5

Add 16 and 5 to get 21.

c=21

Assuming the coin is not weighted and is a fair and standard coin - the chance of flipping head is 1/2. You can either flip head or tails, there are no other possible outcomes.

Answer:

Quadrant II.

Step-by-step explanation:

Quadrant | has positive x and y coordinates.

Quadrant || has negative x and positive y coordinates.

Quadrant ||| has negative x and y coordinates.

Quadrant |V has positive x and negative y coordinates.

Since -3 is negative and 15 is positive, the answer is Quadrant II.

Answer:

873

Step-by-step explanation:

so the equation is: 5x+1

sum is:

[tex] \frac{first \: one \: + \: last \: one}{2} \times quantity \: of \: terms \\ [/tex]

we have 6( 5×1+1) to 91 (5×18+1)

so we have 18 terms

then:

[tex] \frac{91 + 6}{2} \times 18 = 873[/tex]

Answer:

[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]  

The p value for this case would be given:

[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]

The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51

Step-by-step explanation:

Info given

50, 53, 55, 43, 50, 47, 58.

We can calculate the sample mean and deviation with this formula:

[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2)}{n-1}}[/tex]

represent the mean height for the sample  

[tex]s=5.014[/tex] represent the sample standard deviation for the sample  

[tex]n=7[/tex] sample size  

represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean is equal to 51, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 51[/tex]  

Alternative hypothesis:[tex]\mu \neq 51[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing we got:

[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]  

The p value for this case would be given:

[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]

The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51

Answer:

1/8

Step-by-step explanation:

Total cards = 8

Card with 4 = 1

P(4) = 1/8

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The rectangle has an area of 60 square feet. Find its dimensions (in ft) if the length of the rectangle is 4 ft more than its widh.

smaller value ___________________ ft

larger value ____________________ ft

Answer:

Smaller value = 6 ft

Larger value = 10 ft

Step-by-step explanation:

Recall that the area of a rectangle is given by

[tex]Area = W \times L[/tex]

Where W is the width and L is the length of the rectangle.

It is given that the rectangle has an area of 60 square feet.

[tex]Area = 60 \: ft^2 \\\\60 = W \times L \\\\[/tex]

It is also given that the length of the rectangle is 4 ft more than its width

[tex]L = W + 4[/tex]

Substitute [tex]L = W + 4[/tex] into the above equation

[tex]60 = W \times (W + 4) \\\\60 = W^2 + 4W \\\\W^2 + 4W - 60 = 0 \\\\[/tex]

So we are left with a quadratic equation.

We may solve the quadratic equation using the factorization method  

[tex]W^2 + 10W - 6W - 60 \\\\W(W + 10) – 6(W + 10) \\\\(W + 10) (W - 6) = 0 \\\\[/tex]

So,

[tex](W + 10) = 0 \\\\W = -10 \\\\[/tex]

Since width cannot be negative, discard the negative value of W

[tex](W - 6) = 0 \\\\W = 6 \: ft \\\\[/tex]

The length of the rectangle is  

[tex]L = W + 4 \\\\L = 6 + 4 \\\\L = 10 \: ft \\\\[/tex]

Therefore, the dimensions of the rectangle are

Smaller value = 6 ft

Larger value = 10 ft

Verification:

[tex]Area = W \times L \\\\Area = 6 \times 10 \\\\Area = 60 \: ft^2 \\\\[/tex]

Hence verified.

Answer:

option 1

Step-by-step explanation:

[tex]r=\sqrt{(5\sqrt{2})^{2}+(-5\sqrt{2})^{2} } \\\\=\sqrt{25*2+25*2}\\\\ =\sqrt{50+50}\\\\=\sqrt{100}\\\\=10[/tex]

[tex]x=tan^{-1}(\frac{-5\sqrt{2}}{5\sqrt{2}})\\\\x=tan^{-1} (-1)\\x=\frac{7\pi}{4}[/tex]

[tex]re^{ix}=10e^{i\frac{7\pi}{4}}[/tex]

Answer:

we dont see aa figure

Step-by-step explanation:

Answer:

A digit that makes this sentence true is 4.

Step-by-step explanation:

Since the first digit in the number to the left is 3, you simply have to find a digit greater than 3. Here are the possibilities:

4

5

6

7

8

and

9

Out of any of these you can choose, I chose 4.

9514 1404 393

Answer:

   3, or any greater digit

Step-by-step explanation:

Suppose the digit is 'd'. Then the value on the right is ...

  69.436 +100d

Subtracting the value on the left, we want the difference greater than 0.

  69.436 +100d - 352.934 > 0

  100d -293.498 > 0 . . . . simplify

  100d > 293.498 . . . . . . . add 293.498

  d > 2.93498 . . . . . . . . . . divide by 100

That is d is any single digit greater than 2.9. Those digits are ...

  d ∈ {3, 4, 5, 6, 7, 8, 9}

Any digit 3 or greater makes the sentence true.

━━━━━━━☆☆━━━━━━━

▹ Answer

2,013 cartons

▹ Step-by-Step Explanation

72,468 ÷ 36 = 2,013 cartons

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

72,468 eggs divided by 36 eggs per carton=2,013 cartons

Step-by-step explanation:

Answer:

Here you go!! :)

Step-by-step explanation:

Given that the sides of the quadrilateral are 3.3

The measure of one angle is 116°

We need to determine the value of x.

Value of x:

Since, the given quadrilateral is a rhombus because it has all four sides equal.

We know the property that the opposite sides of the rhombus are equal.

The measure of the opposite angle is 116°

x = measure of opposite angle

x = 116°

Then, the value of x is 116°

Therefore, the value of x is 116°

Answer:

In the diagram, the measurement of x is 87°

Step-by-step explanation:

In this diagram, this shape is a quadrilateral. This quadrilateral in this picture is known as rhombus. In a rhombus, the consecutive angles are supplementary meaning they have a sum of 180°. Consecutive means the angles are beside each other. So, we will subtract 93 from 180 to find the value of x.

180 - 93 = 87

The measurement of x is 87°

Answer:

  A.  (2, 4)

Step-by-step explanation:

The ordered pairs represent (x, y). Since you have y =2x, this is the same as ...

  (x, 2x)

That is, the second number in the pair needs to be twice the first number in the pair. Since you know your times tables, you know that this is not the case for (1, 0), (10, 5) or (4, 12). Those values of x would give (1, 2), (10, 20), (4, 8).

It is the case that you have (x, 2x) for (2, 4).

The point (2, 4) lies on the graph of y = 2x.

Answer:

[tex]\Large \boxed{\sf \ \ 28 \ \text{ and } \ 62 \ \ }[/tex]

Step-by-step explanation:

Hello, let's note a and b the two numbers.

We can write that

a = 6 + 2b

ab = 1736

So

[tex](6+2b)b=1736\\\\ \text{***Subtract 1736*** } <=> 2b^2+6b-1736=0\\\\ \text{***Divide by 2 } <=> b^2+3b-868=0 \\ \\ \text{***factorize*** } <=> b^2 +31b-28b-868=0 \\ \\ <=> b(b+31) -28(b+31)=0 \\ \\ <=> (b+31)(b-28) =0 \\ \\ <=> b = 28 \ \ or \ \ b = -31[/tex]

We are looking for positive numbers so the solution is b = 28

and then a = 6 +2*28 = 62

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: Anything above 2

Step-by-step explanation:

Answer: 3,4,5,6,7,8,9 (Any of these digits work)

Step-by-step explanation:

We want to find a digit that makes the number greater than 3260.2. There are many digits that can fit in there.

3318.7≥3260.2

Here, we plugged in a 3. that makes this sentence true because 3318.7 is greater than or equal to 3260.2. Since 3 works, we know that any digit greater than 3 would fit.

Answer:

[tex]\boxed{\sf \ \ \ a=-2, \ b = 1 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

saying that the function is continuous means that you cannot have a "jump" in the graph of the function

so we want

a*(-3)+b=7 and a*4+b=-7

it comes

   (1) -3a + b = 7

   (2) 4a + b = -7

(2)-(1) gives 4a + b + 3a - b =7a = -7-7 = -14

so a = -14/7 = -2

we replace in (1)

b = 7 + 3*(-2) = 7 - 6 = 1

hope this helps

Answer:

a. t>w

Step-by-step explanation:

Sin t= 0.29

t = sin^-1(0.29)

t= 16.86°

Sin w= 0.43

W = sin^-1(0.43)

W= 25.47°

Angles in the second quadrant are positive in sine and they are generally determined by subtracting the initial value from 180°

For t= 180°-16.86°

t = 163.14°

For w = 180°-25.47°

W= 154.53°

163.14°>154.53°

t>w