The sum of four consecutive multiples of 7 is 378. Find the numbers

Answer:

[tex]t=46.4\ years[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=?\ years\\P=\$200\\A=\$500\\ r=1.98\%=1.98/100=0.0198\\n=4[/tex]  

substitute in the formula above

[tex]500=200(1+\frac{0.0198}{4})^{4t}[/tex]  

[tex]2.5=(1.00495)^{4t}[/tex]  

Apply property of exponents

[tex]2.5=[(1.00495)^{4}]^t[/tex]  

Apply log both sides

[tex]log(2.5)=log[(1.00495)^{4}]^t[/tex]  

[tex]t=log(2.5)/log[(1.00495)^{4}][/tex]  

[tex]t=46.4\ years[/tex]

Final answer:

To find when the investment of $200 at a 1.98% annual interest rate compounded quarterly will reach $500, we use the compound interest formula and solve for t, representing time in years.

Explanation:

The subject is Mathematics, specifically focusing on the concept of compound interest. To find out when the investment will reach $500, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested for in years.

In the case of the student's question:

P = $200

n = 4 (since the interest is compounded quarterly)

A = $500

We rearrange the formula to solve for t:

t = (log(A/P)) / (n×log(1+r/n))

Substitute the given values:

t = (log(500/200)) / (4×log(1+0.0198/4))

Use a calculator to compute t, which will give us the number of years it takes for the investment to reach $500.

Answer:

There is only graph that starts with a line from y = h(x) = -4. Hence the required graph of the plot of h(x) is given by the second graph.

Therefore the correct option is the second graph.

Step-by-step explanation:

i) h(x) = [tex]\frac{x}{4}[/tex] - 4 for x ≤ 0. Therefore when x = 0 h(x) = -4

 There is only graph that starts with a line from y = h(x) = -4. Hence the required graph of the plot of h(x) is given by the second graph.

ii) For x < 0 we see from the from the equation in i) that h(x) will be more and more negative as the value of x decreases from 0.

iii) h(x) = [tex]\frac{x}{3}[/tex] - 3 for 0 < x ≤ 3 . Therefore when x = 0 , h(x) = -3 and again when x = 3  then x = -2 which is again the condition fulfilled by graph 2.

iv) h(x) = [tex]\frac{x}{2}[/tex] - 2 for x ≥ 4 . Therefore when x = 4 h(x) = 0 and as x increases from 4 we see that h(x) also increases to positive values.

This is also satisfied in the plot shown in the second graph.

v) Therefore the correct option is the second graph.

Answer:

Step-by-step explanation:

B

Answer:

6

Step-by-step explanation:

0.75/0.125 = 6

6 x 0.125 would add up to be 0.75

To divide decimals, move the decimal point in both numbers to turn the divisor into a whole number. Multiply both numbers by the same power of 10 to get rid of the decimals. Then, divide the resulting whole numbers to get the answer.

To divide decimals, we can move the decimal point in both numbers to turn the divisor into a whole number. In this case, we can multiply both numbers by 1000 to get rid of the decimals. So, 0.75 becomes 750 and 0.125 becomes 125. Now, we can divide 750 by 125 to get the answer. Therefore, 0.75 divided by 0.125 is equal to 6.

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Answer:

34

Step-by-step explanation:

We know the straight line is equal to 180°, and the three angles that make it are (x+12),100°, and x. We can use the equation 180=(x+12)+100+x to find x.

180=(x+12)+100+x

We can remove the parentheses and combine x plus x to 2x.

180=100+2x+12

100+12=112

so

180=112+2x

-112 -112

68=2x

÷2 ÷2

34=x

Answer:

116

Step-by-step explanation:

2+2+5+3+6+4+6+2+5+78+2+1

4+5+3+6+4+6+2+5+78+2+1

9+3+6+4+6+2+5+78+2+1

12+6+4+6+2+5+78+2+1

18+4+6+2+5+78+2+1

22+6+2+5+78+2+1

28+2+5+78+2+1

35+78+2+1

113+2+1

116

Answer:

116

Step-by-step explanation:

60 percent of 78 is the same as 65 percent of 72.

Step-by-step explanation:

Let,

x be the unknown number.

According to given statement;

60% of 78 = 65% of x

[tex]\frac{60}{100}*78=\frac{65}{100}x\\0.60*78=0.65*x\\46.8=0.65x\\0.65x=46.8\\[/tex]

Dividing both sides by 0.65

[tex]\frac{0.65x}{0.65}=\frac{46.8}{0.65}\\x=72[/tex]

Therefore;

60 percent of 78 is the same as 65 percent of 72.

Keywords: percentage, division

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Answer:

72

Step-by-step explanation:

sheesh kinda bussing

btw shesh

Answer:DE and BC

Step-by-step explanation:

Answer:

i dont know to be honest but i hope someone gives you the right answer that your looking for

Step-by-step explanation:

The missing number in the expression 5/8 + 2/? = 1 1/40 is 5. This was found by first converting the mixed number to an improper fraction and solving for the unknown denominator by finding a common denominator and simplifying the equation.

The question asks to find the missing number in the fraction equation 5/8 + 2/? = 1 1/40. To find the missing denominator, we can first convert the mixed number to an improper fraction, making the equation 5/8 + 2/? = 41/40. We then want the expression on the left to equal 41/40.

To begin, let's solve for the missing denominator by assuming it is 'x'. So, our equation is 5/8 + 2/x = 41/40. We need to get a common denominator to be able to add the fractions. The common denominator for 8, x, and 40 would be 40x. Now we multiply both sides by 40x to clear the fractions:

40x*(5/8) + 40x*(2/x) = 40x*(41/40)

Which simplifies to:

5*5x + 80 = 41x

Now, we move like terms to one side to solve for x:

80 = 41x - 25x

Which simplifies to:

80 = 16x

Dividing both sides by 16 gives us:

x = 5

Therefore, the missing number in the original equation is 5.

Jason needs to ride 0.75 miles more to reach the end of the path

Solution:

Given that Jason begins at the start of a path and rides his bike [tex]11\frac{1}{2}[/tex] miles on the path

From given information,

[tex]\text{Total length of path } = 12\frac{1}{4} \text{ miles } = \frac{4 \times 12 + 1}{4} = \frac{49}{4} \text{ miles }[/tex]

[tex]\text{Distance covered already } = 11\frac{1}{2} \text{ miles } = \frac{11 \times 2 +1}{2} = \frac{23}{2} \text{ miles }[/tex]

To find: Distance in miles Jason must ride to reach the end of the path

Thus subtracting distance already covered from total distance, we get the distance Jason must ride to reach the end of the path

[tex]\text{Distance needed } = \text{Total length of path } - \text{Distance already covered }\\\\\text{Distance needed } = \frac{49}{4} - \frac{23}{2}\\\\\text{Distance needed } =\frac{49}{4} - \frac{23 \times 2}{2 \times 2}\\\\\text{Distance needed } =\frac{49}{4} - \frac{46}{4} = \frac{49-46}{4} = \frac{3}{4} = 0.75[/tex]

Thus Jason needs to ride 0.75 miles more to reach the end of the path

[tex]1\frac{2}{3}[/tex] can be rewritten as 5/3 which is improper fraction.

A fraction represents a part of a whole.

Fractions are three types, Proper, improper and mixed fractions.

In proper fractions, denominator is less than numerator.

Improper fractions are fractions whose denominator is greater than numerator.

Mixed fractions can be converted to improper fractions.

The given fraction is improper fraction.

[tex]1\frac{2}{3}[/tex] is a mixed fraction.

((3×1)+2))/3=5/3

Hence, [tex]1\frac{2}{3}[/tex] can be rewritten as 5/3 which is improper fraction.

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Answer:

18.18 miles.

Step-by-step explanation:

A truck uses 1 tablespoon of gasoline to drive 125 yards.

Now, 1 gallon of gasoline contains 256 tablespoons of gasoline.

So, the truck uses 1 gallon i.e. 256 tablespoons of gasoline to drive (256 × 125) = 32000 yards.

Now, 1-mile distance contains 1760 yards.

Therefore, the truck uses 1 gallon of gasoline to drive [tex]\frac{32000}{1760} = 18.18[/tex] miles. (Answer)  

Joyce: y = 2x + 7

Haley: y = 3x

From looking at these two equations, we can assume that Haley will eventually catch up and pass Joyce because she sells items for $3 whereas Joyce had a head start of $7, but only sells items for $2.

Using substitution, we plug in y = 3x into y in the first equation: 3x = 2x + 7

This leaves us at x = 7.

y = 3(7) or 21.

The point at which Haley's and Joyce's money will be exactly the same is (7, 21). After this point, Haley will have more money.

Answer:

The statement that is true about deep currents is :

They move cold water along the bottom of the ocean from the Atlantic Ocean to the Pacific Ocean.

The correct option for this is the second option, Option B.

Step-by-step explanation:

The statement that is true about deep currents is :

They move cold water along the bottom of the ocean from the Atlantic Ocean to the Pacific Ocean.

Answer:

6. a=22, b= 11

7. a =4, b=

[tex]2 \sqrt{2} [/tex]

Step-by-step explanation:

6.

[tex] \tan(30) = \frac{b}{11 \sqrt{3} } \\ or \: \: ( \frac{1}{ \sqrt{3} } ) = \frac{b}{11 \sqrt{3} } \\ or \: \: \: b = 11 \\ and \: \sin(30) = \frac{11}{a} \\ or \: \ \: \frac{1}{2} = \frac{11}{a} \\ \: \: \: \: a = 22[/tex]

Hope u understand....

Answer:

1. 22 * 3 = t

2. 4 + 7 = f

Step-by-step explanation:

Addison brought 66 treats to school and Brady caught 11 fish last weekend.

To determine how many treats Addison brought to school, we can write the following equation: t/22 = 3, where t represents the number of treats. To solve for t, we can multiply both sides of the equation by 22 to get t = 3 * 22 = 66. Therefore, Addison brought 66 treats to school.

To determine how many fish Brady caught last weekend, we can write the equation: f - 4 = 7, where f represents the number of fish. To solve for f, we can add 4 to both sides of the equation to get f = 7 + 4 = 11. Therefore, Brady caught 11 fish last weekend.

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Answer:

Step-by-step explanation:

f(x) = -4x^2 - 6x - 1  ........ g(x) = -x^2 - 5x + 3

find (f + g)(x)

-4x^2 - 6x - 1 + (-x^2 - 5x + 3) =

-4x^2 - 6x - 1 - x^2 - 5x + 3 =

-5x^2 - 11x + 2 <====

Answer: B

Step-by-step explanation:

Answer:

[tex]m\angle RST=41^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The measure of the external angle is the semi-difference of the arcs it covers.

so

[tex]m\angle RST=\frac{1}{2}[arc\ RT-arc\ UV][/tex]

substitute the given values

[tex]m\angle RST=\frac{1}{2}[107^o-25^o][/tex]

[tex]m\angle RST=\frac{1}{2}[82^o][/tex]

[tex]m\angle RST=41^o[/tex]

Answer:

cos θ = -(√3)/2

tan θ = -1/√3

Step-by-step explanation:

[tex]\frac{\pi }{2} <\theta <\pi \ \ \ sin \ \theta = \frac{1}{2} \\[/tex]

Part A: find cos θ:

Using Pythagorean identity

sin²θ + cos²θ = 1

cos²θ = 1 - sin²θ = 1 - (1/2)² = 1 - 1/4 = 3/4

cos θ = ±√(3/4) = ±(√3)/2

∵(π/2) < θ < π  ⇒ ∴ cos θ = -(√3)/2

Part B: find tan θ:

sec θ = 1/(cos θ) = -2/√3

Using Pythagorean identity

tan²θ + 1 = sec²θ

tan²θ = sec²θ - 1 = 4/3 - 1 = 1/3

tan θ = ±√(1/3) = ± 1/√3

∵(π/2) < θ < π  ⇒ ∴ tan θ = -1/√3

Answer: 75

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

multiple of 15

7+5=12

Answer:

5/26

Step-by-step explanation:

red / all = 10 / (15+5+10+12 +10)

=10 / 52

=5/26

Probability of choosing a red candy is 5 / 26

Given that:

Number of brown candy = 15

Number of blue candy = 10

Number of red candy = 10

Number of green candy = 5

Number of yellow candy = 12

Find:

Probability of choosing a red candy

Computation:

Total number of candies = 15+5+10+12+10

Total number of candies = 52

Probability of choosing a red candy = Number of red candy / Total number of candies

Probability of choosing a red candy = 10 / 52

Probability of choosing a red candy = 5 / 26

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Answer:

800

Step-by-step explanation:

1400 (the whole) / 7 (the whole) =200 (the partial) 200*4=800

Answer:

800

Step-by-step explanation:

4 out of 7 equals x out of 1400?

4/7 = x/1400

Cross multiply.

7x = 4 * 1400

Divide both sides by 7.

x = 4 * 1400/7

x = 4 * 200

x = 800

Answer: 800 dentists

Answer:

[tex]a^n=x[/tex]

Step-by-step explanation:

The complete question is in the attachment.

We want to find an expression that is equivalent to: [tex]\sqrt[n]{x} =a[/tex]

Note that: [tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex]

This implies that:

[tex]x^{\frac{1}{n}}=a[/tex]

Or

[tex]x^{\frac{1}{n}}=a^1[/tex]

[tex]x^{\frac{1}{n}*n}=a^{1*n}[/tex]

This simplifies to:

[tex]x=a^n[/tex]

Answer: The answer is X^n = a

Step-by-step explanation:

Got it right!

Answer:

5% less of 180, or 95% of 180

Step-by-step explanation:

FInd 10% of 180, 18, multiply 18 by 9.

18 x 9 = 162, find half of 18 which is 9.

Add to 162.

162 + 9 = 171.

Therefore,

5% less of 180 is 171.

Answer:

Using ounces, the inequality should be:

15c + 70b < 112,000

Using pounds, the inequality should be:

0.9375c + 4.375b < 7,000

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Weight of a can of soft drink (c) = 15 ounces

Weight of a bottle of soft drink (b) = 70 ounces

The truck mist be carrying less than 7,000 pounds

2. Find the inequality describing this.

Let's recall that 1 pound = 16 ounces and 1 ounce = 0.0625 pounds

c = Number of cans in the truck

b = Number of bottles in the truck

Upon saying that, we can write the inequality either using ounces or pounds, this way:

Using ounces, the inequality should be:

15c + 70b < 7,000 * 16

15c + 70b < 112,000

Using pounds, the inequality should be:

15 * 0.0625c + 70 * 0.0625b < 7,000

0.9375c + 4.375b < 7,000

Answer:

The possible distance in miles that Amelia can drive without exceeding her budget is 270 miles

Step-by-step explanation:

Given:

Amelia's budget for renting a car for a day trip = $ 89

Rental cost  = $35

cost per mile  = $0.20

To Find:

The possible distance in miles that Amelia can drive without exceeding her budget = ?

Solution:

Let M be the number of miles

The equation representing the situation can be

Total budget  less than or equal to rental + (number of mile x cost per mile)

That is

[tex]89 \leq 35 +(0.20 \times M)[/tex]

Solving for M, we get

[tex]89-35 \leq 0.20 M\\[/tex]

[tex]54 \leq 0.20M\\[/tex]

[tex]M \leq \frac{54}{0.20}[/tex]

[tex]M \leq 270[/tex]

Amelia's budget: $89. Rental: $35/day + $0.20/mile. Inequality: [tex]\( M \leq 270 \)[/tex] . Amelia can drive ≤270 miles.

let's break it down step by step.

1. Setting up the total cost equation:

  We're given that the rental cost is $35 per day plus $0.20 per mile. So, the total cost [tex]\( C \)[/tex] can be represented as:

 [tex]\[ C = 35 + 0.20M \][/tex]

  Where [tex]\( M \)[/tex] is the number of miles driven.

2. Setting up the inequality:

  We're told that Amelia can spend no more than $89. Therefore, we set up the inequality:

 [tex]\[ 35 + 0.20M \leq 89 \][/tex]

  This inequality represents that the total cost (rental cost plus mileage cost) should be less than or equal to $89.

3. Solving the inequality:

  To solve for [tex]\( M \),[/tex] we first subtract $35 from both sides to isolate the term involving [tex]\( M \):[/tex]

 [tex]\[ 0.20M \leq 89 - 35 \] \[ 0.20M \leq 54 \][/tex]

4. Dividing both sides by 0.20 to isolate [tex]\( M \):[/tex]

  [tex]\[ M \leq \frac{54}{0.20} \] \[ M \leq 270 \][/tex]

5. Interpreting the result:

  The inequality [tex]\( M \leq 270 \)[/tex] tells us that Amelia can drive at most 270 miles without exceeding her budget of $89.

So, in detail, Amelia can drive a maximum of 270 miles to stay within her budget. Any distance beyond that would exceed her budget of $89 for the day trip.

Answer:

Answer is D

Step-by-step explanation:

10x+5y

10(6)+5(9)

60+45=

105

Answer:

Statement (reason):

∆ABC is an isosceles triangle with vertex angle B (Given).

Angle A is congruent to angle E (Given).

Angle BCA is congruent to angle DCE (Given).

BC is congruent to DC (Given).

∆ABC is congruent to ∆EDC (AAS).

AC is congruent to CE (CPCTC).

C is the midpoint of AE (Definition of midpoint).

Answer: x² + y² + 22x + 16y + 169 = 0

Step-by-step explanation:

Equation of a circle with center (a,b) , and radius r i.e center is  not the origin

The equation becomes

( x - a )² + ( y - b )² = r² ------------------------------ 1

a = -11, b = -8

[( x - (-11 )]²  +  [( y - (-8)]² = 4²

      ( x + 11 )² + ( y + 8 )² = 4²

Carry out expansion

x² + 22x + 121 +  y² + 16y + 64 = 16

Rearrange the expression,

x² + y² + 22x + 16y + 121 + 64 - 16 = 0

x² + y² + 22x + 16y + 169 = 0

The equation of the circle is

x² + y² + 22x + 16y + 169 = 0