In Alaska, the temperature can get cold really quickly. Yesterday, the temperature dropped 3 degrees for 9 hours straight. What is the total temperature change during the 9 hours?

Answer:

The value of b is 12.9 cm

The value of a is 15.3 cm

Step-by-step explanation:

see the attached figure to better understand the problem

Find the value of b

we know that

in the right triangle ABC

The function sine of angle of 40 degrees is equal to divide the opposite side to the angle of 40 degrees (AC) by the hypotenuse (AB)

so

[tex]sin(40\°)=AC/AB[/tex]

Solve for AC

[tex]AC=(AB)sin(40\°)[/tex]

substitute the given value

[tex]AC=(20)sin(40\°)[/tex]

[tex]AC=12.9\ cm[/tex]

therefore

The value of b is 12.9 cm

Find the value of a

we know that

in the right triangle ABC

The function cosine of angle of 40 degrees is equal to divide the adjacent side to the angle of 40 degrees (BC) by the hypotenuse (AB)

so

[tex]cos(40\°)=BC/AB[/tex]

Solve for BC

[tex]BC=(AB)cos(40\°)[/tex]

substitute the given value

[tex]BC=(20)cos(40\°)[/tex]

[tex]BC=15.3\ cm[/tex]

therefore

The value of a is 15.3 cm

Answer:

C. [tex]h(x)=x-3[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=x+3[/tex]. We are asked to find the inverse of the given function.

First of all, we will replace [tex]f(x)[/tex] by y as:

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

Now, we will interchange x and y variables as:

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

Solve for y:

[tex]x-3=y+3-3[/tex]

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

Switch sides:

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

Therefore, the inverse function for the given function would be [tex]h(x)=x-3[/tex].

Answer:

C

Step-by-step explanation:

Answer:

The vertical distance is 25.825 ft

Step-by-step explanation:

we know that

To find out the vertical distance between Cece and the base of the mountain, subtract the height of the base of the mountain from the height of Cece

Let

x -----> the height of Cece

y ----> the height of the base of the mountain

we have

[tex]x=15\frac{5}{8}\ ft[/tex] ----> is positive because is above sea level

convert to an improper fraction

[tex]x=15\frac{5}{8}\ ft=\frac{15*8+5}{8}=\frac{125}{8}=15.625\ ft[/tex]

[tex]y=-10.2\ ft[/tex] -----> is negative because is below sea level

so

[tex]x-y=15.625-(-10.2)=15.625+10.2=25.825\ ft[/tex]

Remember that -1*(-1)=+1

Answer:

The running club has 35 members

Step-by-step explanation:

Let

x ----> the total members of the running club

we know that

The total members of the running club multiplied by 5/7 plus 6 must be equal to 31 people

so

[tex]\frac{5}{7}x+6=31[/tex]

Solve for x

[tex]\frac{5}{7}x=31-6[/tex]

[tex]\frac{5}{7}x=25[/tex]

[tex]x=25(7)/5[/tex]

[tex]x=35\ members[/tex]

therefore

The running club has 35 members

Probability of a male having a blood circulation problem, given he's a smoker, is approximately 0.6667.

Step 1:

Identify the given probabilities:

Let [tex]\( P(A) \)[/tex] be the probability that a randomly chosen male has a blood circulation problem, which is [tex]\( 0.25 \)[/tex].

Let [tex]\( P(B|A) \)[/tex] be the probability that a male is a smoker given that he has a blood circulation problem, and it's twice the probability of being a smoker given not having a blood circulation problem.

Step 2:

Calculate [tex]\( P(B|\neg A) \)[/tex]:

Since males with blood circulation problems are twice as likely to be smokers as those without, \( P(B|\neg A) \) is half of [tex]\( P(B|A) \)[/tex], which is [tex]\( \frac{1}{2} \)[/tex].

Step 3:

Apply Bayes' theorem:

[tex]\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \][/tex]

Step 4:

Calculate \( P(B) \):

[tex]\[ P(B) = P(B|A) \times P(A) + P(B|\neg A) \times P(\neg A) \][/tex]

Step 5:

Substitute values into Bayes' theorem and solve:

[tex]\[ P(A|B) = \frac{(2 \times P(B|\neg A)) \times P(A)}{(2 \times P(B|\neg A)) \times P(A) + P(B|\neg A) \times (1 - P(A))} \]\[ P(A|B) = \frac{(2 \times \frac{1}{2}) \times 0.25}{(2 \times \frac{1}{2}) \times 0.25 + \frac{1}{2} \times (1 - 0.25)} \]\[ P(A|B) = \frac{0.25}{0.25 + 0.125} \]\[ P(A|B) = \frac{0.25}{0.375} \]\[ P(A|B) \approx 0.6667 \][/tex]

Thus, the probability that a male has a blood circulation problem, given that he is a smoker, is approximately 0.6667.

3y-14=13

move -14 to the other side

sign changes from -14 to +14

3y-14+14=13+14

3y=13+14

3y=27

divide both sides by 3 to get y by itself

3y/3=27/3

Answer: y=9

Answer:

A is the answer. 2(n+2)

Answer:

A

Step-by-step explanation:

The sum of a number n and 2 is n + 2

Twice this sum is

2(n+ 2) → A

Answer: 36

Step-by-step explanation:

5x has to equal 180 and 180 divided by 5 equals 36. This means that x=36 and 4x=144

Answer: B. 36

Step-by-step explanation:

Look at the answer choices. The one that is an obtuse angle, 144, is going to be divided by 4. Your answer is B. 36

Answer:

42.4285714286

Step-by-step explanation:

If you divide 7.5 by 5/6, the answer comes out to 9. If you multiply 4 5/7 by 9, the answer is 42.4285714286.

Answer:

y=6

Step-by-step explanation:

8y-5y-2=16

8y-5y=16+2

3y=18

y=18/3

y=6

Hey!

------------------------------

Solution:

8y - (5y + 2) = 16

3y - 2 = 16

3y + (-2) + 2 = 16 + 2

3y = 18

3y/3 = 18/3

y = 6

------------------------------

Answer:

y = 6

------------------------------

Hope This Helped! Good Luck!

Answer:

[tex]60[/tex]

Step-by-step explanation:

Suzzane can work 10 math problems in 15 minutes. We need to use proportion and raito.

One hour and a half is equal to 90 minutes. But to equal out the math problem, change it to 900.

So:

[tex]\frac{10}{15}[/tex]  [tex]= \frac{x}{900}[/tex]

[tex]= 60[/tex]

Answer:

72.5 miles/hour

Step-by-step explanation:

When we say "miles per hour" in English this just is simply the question "If Bailey drove for only one hour, how far did she go?". Now mathematically we can find this very easily by simply dividing 290 by 4, which is equal to 72.5. So Bailey travels 72.5 miles every hour.  

If it is confusing about why we do this, think about splitting up 290 miles evenly between 4 hours, how many miles does each hour 'get'. Each would 'get' 72.5 miles. So for every hour Bailey drives she travels 72.5 miles which is the same as saying that she drove at 72.5 miles per hour.

Hope this helps!  

Answer:

Yes

Step-by-step explanation:

A function correlates elements from a set one and only one element from a different set. Think of a train timetable: you can't have the same train in two points at a given time.

An easy way to solve the problem is to take a ruler (or the edge of a sheet of paper, as long as it's straight) and scan the graph parallel to the Y axis. As long as you don't touch the graph more than once, it's a function (zero points is ok!)

Answer:

yes

Step-by-step explanation:

Answer:

6 x 6 x 6

Step-by-step explanation:

Six to the third power means to multiply 6 by itself 3 times.

The standard exponential function is expressed as y = ab^x. The value for the simplified form of 6 to the third power is 216

The standard exponential function is expressed as y = ab^x

Given the following parameters

6 to the third power

This can be expressed as 6^3

6^3 = 6 * 6 * 6

6^3 =36 *6

6^3 = 216

Hence the value for the simplified form of 6 to the third power is 216
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Answer:

206.

Step-by-step explanation:

100x2 = 200

3x2 = 6

200+6 = 206

Answer:

206

Step-by-step explanation:

multiplying anything by 2 is basically adding the exact same number to the original number. So basically: 103 +103

which equals 206

Answer:

3, 6, 12, 24

Step-by-step explanation:

This is a recursive formula which allows the next term in a sequence to be found from the previous term in the sequence

Given

[tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] with a₁ = 3, then

a₂ = 2 × a₁ = 2 × 3 = 6

a₃ = 2 × a₂ = 2 × 6 = 12

a₄ = 2 × a₃ = 2 × 12 = 24

Thus the first 4 terms are 3, 6, 12, 24

Answer:

B.[tex]3,6,12,24[/tex]

Step-by-step explanation:

We are given that

[tex]a_n=2a_{n-1}[/tex]

[tex]a_1=3[/tex]

We have to find the first four terms of G.P

Substitute n=2

[tex]a_2=2a_1=2(3)=6[/tex]

Substitute n=3

[tex]a_3=2a_2=2(6)=12[/tex]

Substitute n=4

[tex]a_4=2a_3=2(12)=24[/tex]

Hence, the first four terms of G.P are  given by

[tex]3,6,12,24[/tex]

Option B is true.

Answer:

B; 2.25

Step-by-step explanation:

Answer:

1/3 mile

Step-by-step explanation:

Answer:

1/3 mile

Step-by-step explanation:

A rectangle strip of land is 2 1/2 miles wide its area is 5/6 square mi.² what is the length of the strip of land

Answer:

x=-3/4

Step-by-step explanation:

Use the distributive property a(a+b)= ab+bc:

-4x-2=1

Add a 2 to both sides:

-4x=3

Divide both sides by -4:

x=3/-4

This can be rewritten as -3/4

[tex]\bf 3\div \cfrac{3}{4}\implies \cfrac{3}{1}\div\cfrac{3}{4}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{1}\cdot \cfrac{4}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 4[/tex]

Answer:

Ian need to keep the website for site B less than 10 months

Step-by-step explanation:

Let

x -----> the number of months

y ----> the cost for website hosting

we know that

Site A

[tex]y=4.95x+49.95[/tex] -----> equation A

Site B

[tex]y=9.95x[/tex] -----> equation B

Equate equation A and equation B and solve for x

[tex]9.95x=4.95x+49.95[/tex]

[tex]9.95x-4.95x=49.95[/tex]

[tex]5x=49.95[/tex]

[tex]x=9.99\ months[/tex]

Round the number of months

[tex]x=10\ months[/tex]

For x=10 months ----> the cost for website hosting is the same in both sites

For x>10 months ---> the cost for website hosting is less expensive in site A

For x<10 months ---> the cost for website hosting is less expensive in site B

therefore

Ian need to keep the website for site B less than 10 months

When comparing the two hosting sites, Site B becomes cheaper than Site A after around 10 months, if the website is kept active during this period. This calculation is made by setting up an equation for the costs and solving for the number of months.

When Ian wants to promote his band on the Internet by creating a website, he needs to make a decision about the cost effectiveness between the two hosting sites. Let's break down the costs for each site:

To find out when Site B would be cheaper than Site A, we need to set up an equation where the left-hand side is the cost for Site A and the right-hand side is the cost for Site B. The equation would therefore be, $49.95 + $4.95n (with n being the number of months) = $9.95n.

To solve for n, subtract $4.95n from both sides leaving $49.95 = $5n. Dividing $49.95 by $5 gives us n = 9.99, which means after around 10 months, Site B becomes cheaper than Site A provided Ian keeps the site active.

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Answer:

$800

Step-by-step explanation:

40*20=800

$800

Answer: 8 x 80

Step-by-step explanation: if you multiply 8 x 80 then you can just act as if the 80 is 8 and once you do the multiplication add the 0 at the end when your done.

Answer:

you got to draw a line cutting the shapes in half, then add the permiters or area of both squares

Step-by-step explanation:

Answer:1-1/3

Step-by-step explanation:

2/3x2=1-1/3

Answer:

3 loaves of banana bread

Step-by-step explanation:

2/3 x 3= 6/3. 6/3 simplified is 2 cups. I hope this helps!

Answer:

Step-by-step explanation:

:  I got A)90

          B)108

          C)333

              Hope that's right. I checked it 4 times.

Answer:

Step-by-step explanation:

A) 90

B) 108

C)333

Answer:

Equation: [tex]3(x-6)^2=12[/tex]

Solutions: [tex]x=4\text{ or }x=8[/tex]

Step-by-step explanation:

Unknown variable [tex]= x[/tex]

Difference of x and 6 [tex]= x - 6[/tex]

Square of the difference of x and 6 [tex]=(x-6)^2[/tex]

Three times the square of the difference of x and 6 [tex]=3(x-6)^2[/tex]

Three times the square of the difference of x and 6 is 12, then

[tex]3(x-6)^2=12[/tex]

Divide this equation by 3:

[tex](x-6)^2 =4[/tex]

Now

[tex]x-6=2\text{ or }x-6=-2\\ \\x=2+6\text{ or }x=-2+6\\ \\x=8\text{ or }x=4[/tex]

Answer:

The answer is x=4 or x=8

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]n,\ n+1-\text{two consecutive numbers}\\\\535-\text{the sum}\\\\\bold{EQUATION:}\\\\n+(n+1)=535\\\\n+n+1=535\\\\2n+1=535\qquad\text{subtract 1 from both sides}\\\\2n+1-1=535-1\\\\2n=534\qquad\text{divide both sides by 2}\\\\\dfrac{2n}{2}=\dfrac{534}{2}\\\\n=267[/tex]

Hey!

--------------------------------

Lets try -10:

2(3(-10) - 1) = 4(-10) - 6

2(-30 - 1) = (-40) - 6

2(-31) = (-40) - 6

-62 ≠ -46

Incorrect.

--------------------------------

Lets try -5:

2(3(-5) - 1) = 4(-5) - 6

2(-15 - 1) = (-20) - 6

2(-16) = (-20) - 6

-32 ≠ -26

Incorrect.

--------------------------------

Lets try -3:

2(3(-3) - 1) = 4(-3) - 6

2(-9 - 1) = (-12) - 6

2(-10) = (-12) - 6

-20 ≠ -18

Incorrect.

--------------------------------

Lets try -1:

2(3(-1) - 1) = 4(-1) - 6

2(-3 - 1) = (-4) - 6

2(-4) = (-4) - 6

-8 ≠ -10

Incorrect.

--------------------------------

So all the options are incorrect.

--------------------------------

Lets solve for x:

2(3x - 1) = 4x - 6

(2 * 3x) + (2 * -1) = 4x + (-6)

6x + (-2) = 4x + (-6)

6x - 2 = 4x - 6

6x - 2 - 4x = 4x - 6 - 4x

2x - 2 = -6

2x + 2 - 2 = -6 + 2

2x = -4

2x/2 = -4/2

x = -2

--------------------------------

Hope This Helped! Good Luck!

Answer:

-1 is the answer

Step-by-step explanation:

Answer:

720 shares

Step-by-step explanation:

Find 60% of 1,200, to figure out how many shares Jillian has.

Change 60% to decimal

0.6

Multiply with the total shares

0.6 x 1,200 = 720

720 shares

Jillian owns 720 shares in a catering corporation.

The percentage is defined as a ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have to determine 60% of 1,200, to figure out how many shares Jillian has.

Convert 60% into a decimal

⇒ 0.6

Multiply with the total shares

⇒ 0.6 × 1200

⇒  720

Hence, Jillian owns 720 shares in a private catering corporation.

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