There was a big snowstorm on Friday night. By Saturday afternoon, 3 inches of the snow had melted. There were still 8 inches of snow left. Solve an equation to find how many inches of snow fell during the snowstorm.

The three sides of the triangle will be 82, 63, and 41 feet.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The perimeter of the triangle is the sum of all three sides of the triangle.

That a flower bed is in the shape of a triangle with one side twice the length of the shortest​ side, and the third side 22 feet more than the length of the shortest side.

Let the three sides of the triangle be A, B, and C. Here A is the longest side B is the shortest side and C is the third side.

Perimeter = A + B + C

A = 2B and C = 22 + B

Put the values in the equation as solve:-

Perimeter = A + B + C

186 = 2B + B + 22 + B

186 = 4B + 22

4B = 186 - 22

4B = 164

B = 164 / 4

B = 41 feet

Longest side = 2B = 2 x 41 = 82 feet

Shirtest side = B = 41 feet

Third side = 22 + B = 22 + 41 = 63 feet

Therefore, the three sides of the triangle will be 82, 63, and 41 feet.

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Answer:

−1≤x<3

Step-by-step explanation:

−4≤3x−1<8

−4≤3x−1and3x−1<8

3x−1≥−4and3x−1+1<8+1

3x≥−3and3x<9

x≥−1andx<3

−1≤x<3

The amount of IRA when he will retire at age 65 = $83448.27

And the total deposits made over the time period is less than the the amount of IRA

We have been given, at age 19​, someone sets up an IRA​ (individual retirement​ account) with an APR of7 ​%. At the end of each month he deposits ​$20.00 in the account.

We need to find the IRA when he retires at age​ 65.

here, 65 - 19 = 46 years

So, the period would be,

46 × 12 = 552 months

Monthly deposit= $20

And the interest rate would be,

Interest = 0.07/12

             = 0.0058

To calculate the future value, we need to use the following formula:

FV= {A × [(1 + i)^n-1]} / i

A= monthly deposit

i = interest rate

n = period

So, the Future Value of Annuity

= 20 × ([1 + 0.0058]^552 - 1 ) / (0.0058)

= 20 × 24.2 / 0.0058

= $83448.27

So, the amount of IRA when he will retire = $83448.27

Deposits made over the time period = 20 × 46 × 12 = $‭11040

Difference = 83448.27 - 11040

= $72408.27

This means, the total deposits made over the time period is less than the the amount of IRA he will get when he retires at age 65.

Therefore, the amount of IRA when he will retire at age 65 = $83448.27

And the total deposits made over the time period is less than the the amount of IRA

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EXPLANATION

Since we have four given scenarios, the only viable option is the third one because It's the only statement where we take a sample (1000 individuals of 1883 participants).

Answer:

When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1.

1 and 3

1 * 12 = 12

2 * 12 = 24

so 1 is true

7 * 5.14 = 36

9 * 5.14 = 46.26

so 2 is not true

7 * 4 = 28

2 * 4 = 8

so 3 is true

In the first case the equation has only one unique solution and in the second case the equation has many solutions.

We are given the equation a|x + b| + c = d and we need to determine the solution of this equation when a > 0 and c = d. The equation contains absolute value symbol which always gives a positive value. The equation can be written as

a|x + b| + c = d

a|x + b| = d - c, since c = d then we can write equation as

a|x + b| = 0, Now, a > 0

=> |x + b| = 0

=> x = -b that is only one unique solution.

Now, in second case a < 0 and c > d then

a|x + b| = d - c

If c > d, then the left-hand side of the equation becomes negative and also a < 0 so the right-hand side also becomes negative. So, the equation will have many solutions in this case.

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the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births is 3/8.

the possible outcomes are

BBB,BBG,BGB,GBB,BGG,GBG,GGB,GGG

wherein 3 meet the requirement. There are 8 possible outcomes, all equally likely (if we assume each gender is equally likely). Hence the choice is 3/8.

We can also think about it in at least one more way: You identified all the possible ways to get 2 boys and one girl. Since the events are disjoint, we can add up the probabilities

P(2 boys, 1 girl)=P(BBG)+P(BGB)+P(GBB)

          =[tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]+ [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex] + [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]

          = 3/8.      

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The cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

As given in the question,

Sale price of the watch for which dealer sold = $39

Let $'x' be the cost of the watch with which dealer purchase

A dealer sold a watch 130% of its cost

Required expression to show the given condition of a dealer is given by:

   130% of x = $39

⇒ (130 /100) × x = $39

⇒ x = ( 39 × 100 ) / 130

⇒ x = $30

Therefore, the cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

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If  the interest rates suddenly rise by 2 percent,  the percentage change in the price of these bonds are : 19.73%, 16.56%.

Using this formula to find the current price of a bond

P=C×1-1(1+YTM)^n/YTM +F /(1+YTM)^n

Where:

P =Current price of a bond

C = Coupon payment,

YTM = Yield to maturity

n = Time to maturity

F =Face value of a bond

The Faulk Corp. bond

C = Coupon rate / number  of payments per year × face value = 4% / 2×$1,000 = $20

n = 13 years = 36 half-year periods

YTM = 7% annually = 7% / 2 = 3.5% semiannually

F = $1,000

hence,

P=20× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36

P=20× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36

P= $405.81 + $289.83

P=$695.61

Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%.

Price of the Faulk Corp. bond:

P=20× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36

P=20× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36

P= $353.32 +$205.03

P=$558.38

Percentage change:

Percentage change = $558.38 - $695.61/$695.61×100%

Percentage change =19.73%

Gonas Company bond:

C =Coupon rate / number of payments per year× face value = 10% / 2 × $1,000 = $50

n = 18 years = 36 half-year periods,

YTM = 7% annually = 7% / 2 = 3.5% semiannually

F = $1,000

P=50× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36

P=50× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36

P= $1,014.52 + $289.83

P=$1,304.35

Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%, bond :

P=50× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36

P=50× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36

P= $883.30 +$205.03

P=$1,088.33

Percentage change:

Percentage change = $1,088.33 - $1,304.35/$1,304.35×100%

Percentage change =16.56%

Therefore the percentage change in the price of these bonds are : 19.73%, 16.56%.

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If there are 189 children, then there are 189 divided 7 = 27 groups of 7 children.

As mentioned in the problem, for every 7 children, there are 2 caretakers therefore, there are a total of 2 x 27 = 54 caretakers in the local daycare.

So, in total, there are 189 children + 54 caretakers = 243 people in the daycare facility.

1) As we were told of the half-life formula along with the data, we can write out the following to get the remains after 170 years:

2) So, according to this model we can tell there will be left approximately

Answer:

  17%

Step-by-step explanation:

You want the percentage represented by a tip of $10.34 on a dinner bill of $61.66.

A percentage is a fraction that has been multiplied by 100%:

  10.34/61.66 × 100%

  ≈ 0.168 × 100%

  ≈ 17%

The tip was about 17% of the original bill.

Here, we want to get the value of x

We can get this by isolating x

We start by bringing like terms together

Answer:

6[tex]x^{2}[/tex]y

Step-by-step explanation:

If I ready your explanation correctly it is

2x3xy  We multiply the 2 and 3 and the xx would be [tex]x^{2}[/tex]

he Solution:

iven in the question that if

We are required to give a counterexample to the given conditional statement above.

Solving each of the equations above, we get

So, the counterexample to the given conditional statement is x = 4.

the multiplication of 2 matrices A and B

a11 a12 a13 ...

a21 a22 a23 ...

a31 a32 a33 ...

...

b11 b12 b13 ...

b21 b22 b23 ...

b31 b32 b33 ...

is

a11×b11+a12×b21+a13×b31+... a11×b12+a12×b22+a13×b32 ...

a21×b11+a22×b21+a23×b31+... a21×b12+a22×b22+a23×b32

a31×b11+a32×b21+a33×b31+... a31×b12+a32×b22+a33×b32

...

in other words, we combine the rows of the first matrix with the columns of the second matrix.

the rows of the result matrix are driven by the rows of the first matrix and the columns of the second matrix.

formally :

we can multiply a m×n matrix only with a n×o matrix.

the number of columns in the first matrix must be equal to the number of rows in the second matrix.

the result matrix is then sized m×o.

the first element (first row first column) of the result matrix is the sum of the products of the elements of the first row of the first matrix with the elements of the first column of the second matrix.

the element in the (x,y) position in the result matrix is the sum of the products of the elements of the xth row of the first matrix with the elements of the yth column of the second matrix.

so, when multiplying 2 2×2 matrices, the condition is automatically fulfilled : m = n = o = 2

ST =

4×0+1×-4 4×4+1×3

-3×0+-2×-4 -3×4+-2×3

=

-4 19

8 -18

and TS =

0×4+4×-3 0×1+4×-2

-4×4+3×-3 -4×1+3×-2

=

-12 -8

-25 -10

as we can see, the 2 results are completely different.

Answer:  3 ≥ W > -5

Step-by-step explanation:

Just look at the way the question is asked, that is the best I can explain. Sorry.

Answer:

[tex]\frac{-5}{2}[/tex]

Step-by-step explanation:

There are two blue dots on the graph.  It does not matter which dot you startr at.  Let's start at the bottom, right dot.  How many space up and to the left you do you have to move to get to the second dot?

You need to move 5 dots straight up.  Up is a positive direction.  Then you have to move 2 spaces left.  Left is a negative direction, so your slope will be negative.

- [tex]\frac{5}{2}[/tex]            [tex]\frac{-5}{2}[/tex]           [tex]\frac{5}{-2}[/tex]   All of these mean the same thing.

Answer:

[tex]t = 18.9[/tex]

Information given :

We know that:

- Element X is a radioactive isotope such that every 20 years, its mass decreases by half

- the initial mass of a sample of Element X is 770 grams

And we must find how long it would be until the mass of the sample reached 400 grams

Step-by-step explanation:

To find it, we need to use the following formula:-

[tex]A(t) = A(0)(0.5)^{\frac{t}{20} }[/tex]

- A(0) is the initial amount

From given information, A(0) = 770 grams

Now, replacing the value in t :

[tex]A(t) = (770)(0.5)^{\frac{t}{20} }[/tex]

Then, we must solve for t :-

[tex]400 = 770(0.5)^{\frac{t}{20} } \\\frac{400}{700}= (0.5)^{\frac{t}{20} } \\\\ 0.51948 = (0.5)^{\frac{t}{20} } \\\\log(0.51948) = log((0.5)^{\frac{t}{20} }) \\\\\\log(0.519,48) = \frac{t}{20} log (0.5)\\t=\frac{20*log(0.519,48)}{log(0.5)} \\t=\frac{20(-0.284431}{-0.301029} \\giving\\t=18.9[/tex]

Hope this helps you out and if does so just mark me as brainliest as this answer took a lot of time to plot down so that it acts as a fuel to your learning,

Stay positive,

a fellow comrade,

Cheers !

The common difference in the given arithmetic sequence is 8.

So, formula for common differences:

Now, insert terms in the formula as follows:

Therefore, the common difference in the given arithmetic sequence is 8.

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Answer:

-5x1/2= -2.5 14x1/8= 1.75

Step-by-step explanation:

-2.5+1.75=-0.75

Answer:

-3/4

Step-by-step explanation:

Plug in values of x and y into expression:

[tex]-5(\frac{1}{2})+14(\frac{1}{8})=[/tex]

[tex]-\frac{5}{2} +\frac{14}{8}=[/tex]

Find common denominator:

[tex]-\frac{5*4}{2*4} +\frac{14}{8}=[/tex]

[tex]-\frac{20}{8} +\frac{14}{8}=\frac{14}{8}-\frac{20}{8}=[/tex]

Solve numerator:

[tex]14-20=-6[/tex]

So,

[tex]=-\frac{6}{8}=-\frac{3}{4}[/tex]

Let's begin by listing out the given information:

The one digit numbers that when added to 746 gives a digit in the ones place of the sum which is less than the ones digit in 746 are;

4, 5, 6, 7, 8, or 9

Place values is the value a digit in a number posseses based on its position in the number

The given parameters of the number are;

The number of digits in the number = 1

The ones digit of the sum of the number and 746 is less than the ones digit in 746, which is 6

Therefore;

The value of the number when added to 746 can be expressed as 7xy

Where;

y < 6

The process of adding two numbers involves the addition of the numbers based on their place values such that the ones digit part of the result is placed as the output while the 1 in a result that is 10 or more is added to the next higher place value number to the left of the added digits

Therefore, to have a value of the digit in the ones place less than 6, we can have;

746 + 0 = 746

746 + 1 = 747

746 + 2 = 748

746 + 3 = 749

The possible one digit numbers that gives a sum with a ones digit less than 6 when added to 746 therefore includes; 4, 5, 6, 7, 8, and 9

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Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types."

Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types." Data concerning categorical variables make up qualitative data.

Quantitative Variables with values obtained through measurement or counting. Variables that exists not measurement variables are referred to as qualitative variables. Their values are not determined by counting or measuring. Values that are used to identify people in a table are called designators. While qualitative research focuses on words and meanings, quantitative research deals with figures and statistics.

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To solve the given system of equation by graphing you only have to graph both lines. The solution is the intersection between the lines.

According to this, the intersection of the two lines is (-2, -2). It means that the solution is (-2, -2).

Answer:

19

Step-by-step explanation:

-3(-7)-2

21-2

19

it need to be at least 20 chqracters so ignore this the answer is at the top