Find the measures of the complementary angles that satisfy each case. The measure of the first angle is 40% less than the measure of the second.

Let x be the amount raised by each club member. Since there are 60 members, the amount raised by them would be

Now, we know the school contributed $1,000. Now, the amount raised is:

Since this amount has to be at least $5,000, we have that the inequality that shows the amount of money that each glee club member needs to raise to help pay for the trip is:

Answer: Option A

If Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.

The total amount he earned = $893

The amount of retainer he earned = $125

The percentage he earned = 30%

30% of the sales = The total amount he earned - The amount of retainer he earned

Substitute the values in the equation

= 893-125

= $768

Consider the total sales as x

Then,

x × (30/100) = 768

0.3x = 768

x = 768/0.3

x = $2560

Hence, if Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.

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since z=6, so z+15 is equal to 21

or a+k+z=21

Answer:

17. s = 9

18. x = 8x^(½)

Step-by-step explanation:

s² - 7 = 74?

s² = 74 + 7

s² = 81

√(s²) = √(81)

s = 9

x² - 8x = 0

x² = 0 + 8x

x² = 8x

√(x²) = √(8x)

x = 8x^(½)

OR by factoring

x²−8x=0

x(x−8)=0

x=0 or x−8=0

x=0 or x=8

Remember that the slope-intercept equation of the line is:

where 'm' is the slope and b is the y-intercept.

In this case, we have the following:

therefore,, the slope is m = 2

Answer:

y=5

Step-by-step explanation:

RS  +    ST   =    RT

9y+2     +     2y+3       =   60

11y         +      5         = 60

11y   =     55

Y = 5

Using a quadratic function, it is found that:

a) The coordinates of the second x-intercept are: (50,0).

b) The vertex shows the maximum flight of the projectile.

c) The coordinates of the vertex are (25, 62).

3) The graph of the equation y = -0.0992(x² - 50x) is given at the end of the answer.

A quadratic function has two x-intercepts, x' and x'', and is defined as follows:

y = a(x - x')(x - x'').

The intercepts are given as follows:

The vertex is found as follows:

Hence the coordinates are: (25, 62).

The equation can be defined as follows:

y = ax(x - 50)

y = a(x² - 50x).

When x = 25, y = 62, hence the leading coefficient is found as follows:

62 = a(25² - 50(25))

-625a = 62

a = -62/625

a = -0.0992.

Hence the equation is:

y = -0.0992(x² - 50x).

The domain of the function is between the roots, hence 0 ≤ x ≤ 50, and the graph is sketched at the end of the answer.

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Answer:

(1,3)

Step-by-step explanation:

You can use the distance formula to help you solve the answer

Answer:

(1; 3)

Step-by-step explanation:

x = (-1 + 3)/2 = 1

y = (6 + 0)/2 = 3

Answer:

x > 7

Step-by-step explanation:

x = 28 ÷ 4

x > 7

that's it

Hey there!

4x > 28
DIVIDE 4 to BOTH SIDES

4x/4 > 28/4

SIMPLIFY it

x > 28/4

x > 7

It is an open circle started at 7 & it’s going to the left of the number line

Therefore, your answer should be:

x > 7

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Solution:

LCM of 9 and 19 is the smallest number among all common multiples of 9 and 19.

The first few multiples of 9 and 19 are (9, 18, 27, 36, 45, 54, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively.

There are 3 commonly used methods to find LCM of 9 and 19 - by listing multiples, by division method, and by prime factorization.

To calculate the LCM of 9 and 19 by the division method, we will divide the numbers(9, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 19.

In this case, we get:

Then, the LCM would be:

so that, the correct answer is:

The mixed fraction of the given improper fraction is [tex]1\frac{2}{5}[/tex].

According to the question,

We have the following improper fraction:

7/5

Now, to convert this into mixed fraction we will divide the numerator by the denominator and add the quotient before the fraction and the remainder will form the numerator and the denominator will remain same as that of this improper fraction.

(More to know: there are three kinds of fraction: proper fraction (in proper fraction, we have denominator larger than numerator), improper fraction and mixed fraction.

So, we will divide 7 by 5:

[tex]1\frac{2}{5}[/tex]

Hence, the mixed fraction of 7/5 is [tex]1\frac{2}{5}[/tex].

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The given expression is

First, we change 1/3 for its reciprocal to transform the division into a product.

Then, we multiply the fractions.

At last, we transform the fraction into a mixed fraction.

Answer:

p = 20

Step-by-step explanation:

7 + 3(p - 1) = 64 ( subtract 7 from both sides )

3(p - 1) = 57 ( divide both sides by 3 )

p - 1 = 19 ( add 1 to both sides )

p = 20

The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.

There could be only two terms, but there could be one hundred, a thousand, or a million.

Here are always an integer number of terms in a summation.

As per the given,

Length of the trench on the first day = 18/20 meters

Length of the trench on the second day = 9/20

Total length of the trench = 18/20 + 9/20

Take LCM as 20

⇒ (18 + 9)/20 = 27/20

⇒ 1.35 which is closest among the given option by 1 1/2 meters.

Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".

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The value of f¹(x) = x/5

What is function?

A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

We are given f(x) = 5x

and we are to find inverse of f(x).

Replace f(x) by y.

So,

y = 5x

Isolate x

x = y/5

Replace x by f'(y)

So,

f'(y) = y/5

Replace all occurrences of y by x.

So,

f'(x) = x/5

Therefore, the inverse of function f(x) = 5x is f'(x) = x/5

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The sum of  -1 (3/4) and 2 (1/2) is the same as the difference between 2 (1/2) and 1 (3/4).

Firstly, we will convert the mixed fractions into improper fractions.

-1 and 3/4 = -7/4

2 and 1/2 = 5/2

Addition of -1 (3/4) and 2 (1/2) = -7/4 + 5/2 = -7/4 + 10/4 = 3/4

Difference between  2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4

As both the values equal to 3/4 , we can say that the addition of  -1  and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.

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Answer:

c = 23

Step-by-step explanation:

To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.

(2c + 51)° = 97°

Next, you want to subtract 51 from both sides.

(2c + 51) - 51 = 97 - 51

2c = 46

Lastly, you isolate c by dividing 46 by 2.

c = 46 ÷ 2

c = 23

two lines are perpendicular when their slope is inverted and have the opposite sign

the general form of the equation line is-3,1

where m is the slope

rewrite

so, the slope 3/8

the slope of the other line is

to write the new equation of the line we use the slope and replace the point (-3,1)

now, replace b and the slope to create the line

Answer:

Step-by-step explanation:

Answer:

6 and 16

Step-by-step explanation:

→ Find the most recurring number in sequence A

6

→ Find the most recurring number in sequence B

16

Answer:

$754.92

Step-by-step explanation:

699.00 plus 8% of 699.00 is 754.92

Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams. 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

Given that,

The 1982 change in pennies composition from all copper to zinc with copper coating was made by the US Mint. Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams.

We have to find how many coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

An issue of quantity and amount. In this context, the term "amount" refers to weight. The variables should be identified with letters that will make them easy to distinguish: Z for largely zinc and C for all copper. Create weight and quantity equations:

C + Z = 1287

3.1 C + 2.5 Z = 3601.5

By multiplying all three components of the first equation by -2.5 and placing them under the second equation, drawing a line, and then subtracting, you can eliminate the Z using this method.

3.1 C + 2.5 Z =  3601.5

-2.5 C -  2.5 Z = -3217.5

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

0.6 C              =    384      

Divide both sides by .6.

C = 640        

Subtract 640 from 1287.

Z = 647

Therefore, 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

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The total money spent on fruits is $7.03

While at  the fruit stand, Ramon bought the following fruits,

3 pounds of apples that cost $0.89 per pound

4 cantaloupes that each cost $1.09

So, the total amount he spent on the materials he bought without including taxes is,

Total money spent = 3 x ( 0.89 ) + 4 x ( 1.09 )

                                = 2.67 + 4.36

                                = 7.03

The total money spent on fruits is $7.03

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Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]

Step-by-step explanation:

[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]

Notice that in the given sequence the difference between the first two terms is 7 so the solution must be in terms of multiples of 7 plus a constant. The only two options that have this characteristic are first and last ones, for the sum to consider the first term the sum must start for r=0.

Answer: last option.

[tex]4a^{2} -25=0\\(2a-5)(2a+5)=0\\2a-5=0 \\or 2a+5=0\\\\a=\frac{5}{2} \\\\or\\\\a=-\frac{5}{2}[/tex]

IF YOU CHECK CAREFULLY YOU WILL FIND THAT THIS EQAUTION IS MADE OF DIFFERENCE OF SQUARES.

GOODLUCK!!

The probability of no loads occurring during that period is at most 0.3 exists 3.2 years.

Given: Mean time between occurrence = 0.4 year

A number of loads expected to occur during a 4 year period

Period = 4

Mean time = 0.4

Let the formula = Period/Mean Time

The number of loads expected to occur during a 4-year period

= 4/0.4 = 10 loads

B. Probability that more than 11 loads occur during 4 year period

The expected number of loads during 4-year period = 10 (from A above)

mean = 10

Using Poisson distribution,

P(k events in interval)= (λ^k * e^-k)/k!

where: k = 0, 1, 2,3,4, . . ., 11 and λ = 10.

P(k = 0) = (1[tex]0^0[/tex] × [tex]e^{-10[/tex])/0! = 0.000045

P(k = 1) = (1[tex]0^1[/tex] ×  [tex]e^{-10[/tex])/1! = 0.000454

P(k = 2) = (10² ×  [tex]e^{-10[/tex])/2! = 0.00227

P(k = 3) = (10³ ×  [tex]e^{-10[/tex])/3! = 0.007567

P(k = 4) = (1[tex]0^4[/tex] ×  [tex]e^{-10[/tex])/4! = 0.018917

P(k = 5) = (1[tex]0^5[/tex] ×  [tex]e^{-10[/tex])/5! = 0.037833

P(k = 6) = (1[tex]0^6[/tex] ×  [tex]e^{-10[/tex])/6! = 0.063055

P(k = 7) = (1[tex]0^7[/tex] ×  [tex]e^{-10[/tex])/7! = 0.090079

P(k = 8) = (1[tex]0^8[/tex] ×  [tex]e^{-10[/tex])/8! = 0.112599

P(k = 9) = (1[tex]0^9[/tex] ×  [tex]e^{-10[/tex])/9! = 0.12511

P(k = 10) = (1[tex]0^{10[/tex] ×  [tex]e^{-10[/tex])/10! = 0.12511

P(k = 11) = (1[tex]0^{11[/tex] ×  [tex]e^{-10[/tex])/11! = 0.113736

The probability that more than 11 loads occur during a 4-year period is then given by the following Express

1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]

substitute the values in the above equation, we get

= 1 - [0.000045 + 0.000454 + 0.00227 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.12511+ 0.12511 + 0.113736]

simplifying the equation, we get

= 1 - 0.571665 = 0.428335

C. How long must a time period be so that the probability of no loads occurring during that period is at most 0.3

(λ^0 * e^-λ)/0! = 0.3

⇒ e^-λ/1 = 0.3

simplifying the above equation, we get

⇒ e^-λ = 0.3

⇒ -λ = ln 0.3

⇒ -λ = -1.204

⇒ λ = 1.204

The time period = 4 years / 1.204

Time period = 3.2 years

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She calls for 4/5 cup of chocolate

She had 7/3 cups of chocolate.

Maximum number of cakes a baker can make = 2

Answer:

141 degrees

Step-by-step explanation:

The total angle interior of a triangle is 180 degrees. And the 2 angles opposite of x equal it so x=103+38