Question 4 of 10
One spring, a group of students measured rainfall totals at their school. This
chart shows how many inches of rain the students measured each month.
How much total rainfall did they receive at their school that spring?
MONTH
March
April
May
Subtracting Decimals in Word Problems
RAINFALL
1.1
4.1
6.1

The inequality that represents the temperatures at which the gas in the truck will remain in liquid form is;  -40°F < x < 140°F

A)  x is the temperature, and the temperature can't go down to -40°F and so x is greater than -40°F so that the gas doesn't freeze. Finally, x can't go higher than 140°F because the gas will evaporate. Thus, the inequality that represents the temperatures at which the gas in the truck will remain in liquid form is;

-40°F < x < 140°F

B) Open interval of the graph would mean that the interval is from -40°F to < 140°F. However, not equal to means that the gas in the truck can't stay liquid and as such means the coordinate is (-40°F, 140°F)

C) The gas will freeze because it has been said in the question the gas freezes at -40°F and as such if it goes -49°F, then it will freeze because the gas is supposed to stay higher than -40°F.

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If initial deposit is GBP 3000 and the rate is 3.5%,then after 32 years it will reach to GBP 9000.

Given that the initial deposit is GBP 3000 and the rate is 3.5%.

We are required to find the number of years after which the amount will reach to GBP 9000.

Compound interest is basically the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

Amount after compounding=P[tex](1+r)^{n}[/tex], where P is principal ,r is rate of interest and n is number of years.

The number of years can be calculated as under:

9000=3000[tex](1+0.035)^{n}[/tex]

3=[tex](1.035)^{n}[/tex]

[tex](1.035)^{32}[/tex]=[tex](1.035)^{n}[/tex]

By comparing both sides,we will get n=32.

Hence if initial deposit is GBP 3000 and the rate is 3.5%,then after 32 years it will reach to GBP 9000.

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The value of the logarithm log y = 7 for y will be e⁷.

We are given the logarithm problem as:

log y = 7

We need to solve this to find the value of y.

We will use the properties of logarithm for this.

So, we get that

⇒ e ^ log y = e ⁷

Solving it, we will get that:

⇒ y = e⁷

So the value of the logarithm log y = 7 for y will be e⁷.

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The number of sections of board that he can construct will be equal to 7.

We are given that:

A carpenter has 6 boards.

Length of each board = 7 / 8 yard long

Now, we will use multiplication.

Total length of cardboards available = 7 / 8 × 6 yards

Total length = 42 / 8 yards

Total length = 21 / 4 yards.

Now, 3/4 yard sections of board that he can construct will be:

Number of sections of board = 21 / 4 ÷ 3 / 4

Number of sections of board = 21 / 3

Number of sections of board = 7

Therefore, the number of sections of board that he can construct will be equal to 7.

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Step-by-step explanation:

10.

the various sides and line segments have been marked as equal already.

so, SSS proves that both triangles are congruent.

but to reprove things with the midpoint theorem :

remember

the line segment in a triangle connecting the midpoints of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

so,

D, F are the midpoints of BA and BC.

so, AC is parallel to DF and twice as long as DF.

D, E are the midpoints of BA and AC.

so, BC is parallel to DE and twice as long as DE.

E, F are the midpoints of AC and BC.

so, BA is parallel to EF and twice as long as EF.

so, DF = AE = EC

DE = BF = FC

EF = BD = DA

so, the EF of DEF corresponds to DA of ADE.

DF corresponds to AE.

and DE is shared between both triangles.

so, again, all 3 sides correspond 1:1 to sides in the other triangle. and SSS proves they are congruent.

11.

equilateral means all 3 sides are equal :

PS = PT = ST

TSR can only be isoceles (both legs are equal) when

ST = SR

because PM = MQ, M is the midpoint of PQ.

and because of MS || QR, S is the midpoint of PR.

that means PS = SR.

and because PS = ST, ST = SR

therefore, TSR is isoceles.

The probability of P(G1 and G2) will be 1/5.

The probability of at least one green will be 3/10.

The probability for P(G2) (G1) will be 1/100.

They're dependent event

G1= The first card drawn is green

G2= the second card drawn is green

The probability of P(G1 and G2) will be:

= 1/10 + 1/10

= 1/5.

The probability of at least one green will be:

= 1/10 + 1/5

= 3/10

The probability for P(G2) (G1) will be:

= 1/10 × 1/10

= 1/100

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Answer:

  k = 110

Step-by-step explanation:

You want the integer multiple of pi that is the area of 300° of a donut with inner radius 8 cm and outer radius of 14 cm.

The area of a circle is given by the formula ...

  A = πr²

Then the area of the outer circle is ...

  A = π(14 cm)² = 196π cm²

The area of the inner circle is ...

  A = π(8 cm)² = 64π cm²

The area of the whole donut is the difference of these areas:

  whole donut area = (196 -64)π cm² = 132π cm²

The shaded area of the figure represents 300° of the 360° full donut. The area is proportional to the central angle, so the shaded area is ...

  shaded area = (300°/360°)×whole donut area

  shaded area = 5/6 × 132π cm² = 110π cm²

Comparing this to the expression kπ cm², we see that ...

  k = 110

Answer: 106 students

Step-by-step explanation:

In a 1:2 ratio, we can see that there are 2x the amount of students with brown/black hair compared to students with blonde hair.

So taking 212 students, we can divide the number by half to get 106 students.

[tex]\frac{212}{2} = 106[/tex]

Answer:

76

Step-by-step explanation:

76 occurs multiple times in the set, thus deviating from it.

Answer:



Root 

Step-by-step explanation:

Answer:

The distance between (2,8) and (-6,-2)

is √100+64

Step-by-step explanation:

There is no linear relationship between t and d.

So, the student drives a car at 45 miles per hour, so travels 45 miles in an hour.

Therefore, there is no linear relationship between t and d.

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Answer: 103. h<=2 or h>=12

105. No solution

107. -6<x<1

Step-by-step explanation:

103. |h-7|>=5

h-7>=5

h>=12

h-7<=-5

h<=2

h<=2 or h>=12

105. |2x-8|<-10 ==> No solution since absolute value functions are always positive.

107. |10+4x|<14

10+4x<14

4x<4

x<1

10+4x>-14

4x>-24

x>-6

-6<x<1

Answer:

g(-7) = 57

Step-by-step explanation:

note: the editor will not let me use eff of x. I have to use g(x)

Equation

g(x) = -2x^2 -4x + 13

Comment

y is the same thing as g(x) so you are really being asked to find y,

Given

x = - 7

g(-7) means that x is -7

Solution

g(x) = -2(-7)^2 - 4(-7) + 13           Substitute x = - 7 on the right

g(x) = -2*49 + 28 + 13                 Combine

g(x) = -98 + 28 + 13

g(-7) = -57

Answer:

1/4 of the dozen is broken

Step-by-step explanation:

If the vertices of the triangle are J(-3,-5), K(-2,2) and L(1,-4) then its reflection in y axis are J(3,-5), K(2,2) and L(-1,-4)

Given,

The vertices of the triangle = J(-3,-5), K(-2,2) and L(1,-4)

We know,

In reflection in y axis (x,y)  will become (-x,y)

Then the vertices of the reflection in y axis = J(3,-5), K(2,2) and L(-1,-4)

Draw the triangle using the vertices.

Hence, if the vertices of the triangle are J(-3,-5), K(-2,2) and L(1,-4) then its reflection in y axis are J(3,-5), K(2,2) and L(-1,-4)

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The equation of the tangent line to the graph is equal to y = 0.

A line is tangent to a function if and only if the function meets the curve only in one point. The slope of the tangent line can be found by using the first derivative of the curve and the y-intercept is determined from the slope-intercept form of the equation of the line. First, determine the slope of the tangent line:

f'(x) = 12 · x

f'(0) = 12 · 0

f'(0) = 0

Second, find the intercept of the equation of the line:

y = 6 · 0²

y = 0

b = y - m · x

b = 0 - 0 · 0

b = 0

Then, the equation of the tangent line to the graph is equal to y = 0.

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Answer:

  2·2·3 or {1, 2, 3, 4, 6, 12} depending on what you mean

Step-by-step explanation:

You want the factors of 12.

The prime factors of 12 are ...

  12 = 2·2·3 = 2²·3

The product of exponents of the prime factors, each increased by 1, is the number of divisors of 12:

  (2+1)(1+1) = 3·2 = 6 . . . . number of divisors of 12.

Those are ...

  1, 2, 3, 4, 6, 12

__

Additional comment

The word "factors" is often used when "divisors" is intended. An expression is factored when it is expressed as a product of prime factors.

Answer:

-4/9 * 8/5 = (- 4/9) x

-32/45= - 4x /9

-288 = 180x

-8/5

hope it help ya..

☘☘☘...

Answer:

Forty-four and two-hundred fifty-nine thousandths.

Total balance in the account after 7 months is 2849.737$

It is given that Timothy deposits $2780.20 in a savings account

It is given that rate of interest is 4.3 % and it of the simple interest nature.

We are required to find the account balance of Timothy's account in 7 months

We know that formula of simple interest is given by

(principal x rate x time)/100

where principal is the amount put for investing

rate is the rate at which the person is going to earn

time is the time for which the amount is to be invested

Now the time that is given to us in the form of months and hence we must convert it into years form

1 year =12 months

therefore, 7 months = 7/12 years

Now applying this value to calculate the simple interest earned

Let the simple interest be 'SI'

principal = $2780.20

rate = 4.3%

time = 7/12 years

SI= (2780.20x 4.3 x 7)/100 x 12

   = 69.737$

The balance in Timothy's account will be original amount + the simple interest

Total balance after 7 months = 2780.20+69.737

                                                  =2849.937$

Hence total balance in the account after 7 months is 2849.737$

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The temperature will be 44.2f when the plane reaches an altitude of 8,000ft.

So, there is a 1.2f drop in temperature for every thousand feet.

The plane is at 8000 ft then:

So,

The temperature at 8000 ft:

Therefore, the temperature will be 44.2f when the plane reaches an altitude of 8,000 ft.

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Answer: greater than

Step-by-step explanation:17.305[tex]\geq[/tex]17.066

Answer:

Yes

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)

Answer:i think its like 40 or sum like that mb-

Step-by-step explanation:

The value of MN is 14 when the Points L, M, and N are collinear.

As per the question statement, we are supposed to find the possible value of MN when the Points L, M, and N are collinear.

Also, LM=21 and LN=35

As LN is greater than LM, point M has to be in between L and N for practicality and question existence.

[tex]LM+MN=LN\\MN=LN-LM\\LN=35\\LM=21\\MN=35-21\\MN=14[/tex]

Hence final answer is MN = 14

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Answer: 8, 13, 6, 12, 4, 13, 5, 13, 11, 19, 12, 17, 9, 16, 10, 13, 7, 14, 11, 20, 10, 18, 9, 16, 7, 15.

Step-by-step explanation:

¡Aquí tienes!

¡Espero que esto te ayude!

The equilibrium quantity and equilibrium price are 34.62 and 25.42 respectively

The functions are given as

Demand: p^2 + 16q= 1200

Supply function: 300 - p^2 + 10q

Rewrite the demand function as

p^2 + 16q - 1200 = 0

At equilibrium, demand  = supply

So, we have:

p^2 + 16q - 1200 = 300 - p^2 + 10q

Using a graphing calculator, we have:

p = 25.42 and q = 34.62

Hence, the equilibrium quantity and equilibrium price are 34.62 and 25.42 respectively

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Answer: 24, 26, 28

Step-by-step explanation:

a=even integer one.

b=even integer two.

c=even integer three.

a=b-2

b=c-2

a=c-2-2

a=c-4

a+b+c=50+c

c-4+c-2+c=50+c

c+c+c-4-2=50+c

3c-6=c+50

2c-6=50

2c=56

c=28

b=c-2

b=28-2

b=26

a=26-2

a=24

24, 26, 28