The sum of three numbers is 95. The first number is 5 more than the third. The second number is 4 times the third. What are the numbers?

To find the cost of 4 5/7 kg of candy, we divide the cost of 5/6 kg by 5/6 to find the cost of 1 kg. Then, we multiply the cost of 1 kg by 4 5/7 to find the total cost.

To find the cost of 4 5/7 kg of candy, we need to find the cost of 1 kg of candy and then multiply it by 4 5/7. Given that 5/6 kg of candy costs $7.50, we can find the cost of 1 kg by dividing $7.50 by 5/6. So, the cost of 1 kg of candy is $9.00. To find the cost of 4 5/7 kg, we multiply $9.00 by 4 5/7.

To multiply a whole number and a fraction, we first convert the whole number to a fraction by placing it over 1. So, 4 can be written as 4/1. Then, we multiply the numerators (4 x 7 + 5) and the denominators (1 x 7). This gives us 33/7. Finally, we multiply $9.00 by 33/7 to find the cost of 4 5/7 kg of candy.

The cost of 4 5/7 kg of candy is $38.57.

Answer:  -4(7g - 6h)(7g + 6h)

Step-by-step explanation:

Separate the 4 terms into two groups of 2 terms. Then factor out the GCF of each group. You should end up with a common factor in each group - that is one of the factors.  The other factor is what you factored out from each term.

  49g² - 36h²              - 28g - 24h

(7g - 6h)(7g + 6h)          -4(7g + 6h)

They both have a common factor of (7g + 6h)

The terms factored out are (7g - 6h) and -4

So, the factorization is: -4(7g - 6h)(7g + 6h)

Answer:13

Step-by-step explanation:

There are hours 2 will it take to fill the pool if it holds 80,000 gallons.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Two hoses are used to fill a swimming pool.

And, Together they fill the pool at a rate of 3 gallons every 5 seconds.

Hence, Time for to fill 80,000 gallons are,

⇒ Time = 80,000 × 3 / 5

⇒ Time = 16,000 × 3

⇒ Time = 48,000 seconds

⇒ Time = 48,000 / 36,000 hours

⇒ Time = 1.33 hours

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Answer:

EX: f(x) ≥ 0 over the interval [-1, 1].

Final answer:

A valid prediction about a continuous function is that it will have no breaks, jumps, or holes, and will exhibit the intermediate value property. If continuity is ensured, we can expect the function to pass through all intermediate values between any two points within a given interval.

Explanation:

A valid prediction about a continuous function is that the function will not have any breaks, jumps, or holes in its graph. This means that for any value within the domain of the function, we can find a corresponding value in the range, making the function predictable and reliable to analyze. A continuous function has the intermediate value property, which tells us that if the function takes on two values, it must take on every value in between at least once. As such, if we know the function is continuous on an interval, we can predict that it will pass through all the intermediate values between any two points in that interval.

An important concept to consider is the change that would invalidate the continuity of such a function. To illustrate, think about what would happen if our continuous function were to suddenly have a point removed or to have a sudden vertical asymptote introduced. This would create a discontinuity. So, when predicting behaviors of continuous functions, we must ensure there are no such changes or 'breaks' occurring within the interval we are considering.

Final answer:

A discount represents the decrease in the item's price during a sale, leading to consumer savings. When a shopper gets a "good deal," they experience the substitution and income effect, which typically results in an increased quantity demanded of the product.

Explanation:

When buying an object on sale, the discount is the decrease in the price of the item. Economists may refer to the situation of getting a "good deal" on a product when the consumer is able to purchase something at a price lower than what it normally sells for, leading to consumer saving. This occurs due to the substitution effect and the income effect. The substitution effect indicates that when a product is cheaper relative to other products, consumers are likely to purchase more of it. On the other hand, the income effect explains that the decrease in price allows the consumer to buy the same amount of goods while still having extra money to purchase even more goods. Due to both these effects, a decrease in price typically leads to an increase in quantity demanded, which might suggest that the demand for a product is elastic if the quantity demand decreases significantly more than the price increase.

Final answer:

Casey spent $12 on chips that cost $2 per bag, so she bought 6 bags of chips.

Explanation:

Casey bought 5 sandwiches at $6 each, totaling $30 spent on sandwiches. Since she spent $42 in total, we subtract the amount spent on sandwiches from the total amount to find out how much she spent on bags of chips: $42 - $30 = $12 spent on chips. Each sandwich cost three times as much as a bag of chips, so one bag of chips costs $6 / 3 = $2. To find out the number of bags of chips b she bought, we divide the total spent on chips by the cost of one bag: $12 / $2 = 6 bags of chips.

Answer:

I guess it is b= d divided by a - c

Answer:

Step-by-step explanation:

ab+c=d

ab=d-c

b(a)=d-c

b=d-c/a

Answer:

x=6

Step-by-step explanation:

Step-by-step explanation:

1.Find a common denominator shared by all the terms (6 or multiply each term by 6/1) and multiply each term by the lcd.

4x-1=3x+3

2.Then solve

4x-1=3x+3

4x=3x+4

7x=4

x=4/7

Answer:

dang that one was hard wish I could help

Step-by-step explanation:

Answer:

2.084...

Step-by-step explanation:

Just write an non repeating string of any numbers that you think of but not in a pattern which will lie between decimal value of your 2 numbers

Irrational numbers between 2 and 3 include √2, which is approximately 1.414.

Irrational numbers are numbers that cannot be expressed as a ratio of integers. An example of an irrational number between 2 and 3 is √2, which is approximately 1.414. It is not possible to represent √2 as a fraction of two integers.

Answer:

[tex]C=60-4t[/tex]

Step-by-step explanation:

A product costs $60 today.

The price is reduced by $4 a day, so

The genaral formula for the price of the product after t days will be

[tex]C=60-4t[/tex]

An acute angle is any angle smaller than 90 degrees. A right angle is an angle that measures 90 degrees.

Answer:2y(3) +6 +5x(3)

(The numbers in parentheses mean they’re an exponent)

Step-by-step explanation:

Adding like terms means to simply combine terms with the same variable and/or exponent

Since there are three numbers with the same variable (y) they are combined. Since there are three numbers without an exponent/ variable,(the 3 twos) they are combined. There is no other term that can be combined with 5x(3), so you just leave it as is.

Answer:

6950

Step-by-step explanation: multiply 278 times 25

Answer:

A. [tex]\dfrac{1}{25}=0.04[/tex] or 4%

B. [tex]\dfrac{16}{25}=0.64[/tex] or 64%

C. 8 times

Step-by-step explanation:

The county-fair prize wheel has equally spaced sections with the following colors: 1 is golden, 2 are silver, 3 are green, 4 are blue, 6 are red, and 9 are yellow, 25 sections in total.

A. The probability of landing on gold is

[tex]P_1=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}=\dfrac{1}{25}=0.04[/tex]

or 4% as a percent.

B.  If the probability of landing on yellow is 36% (or 0.36 as decimal), then the probability of not landing on yellow is

[tex]P_2=1-0.36=0.64[/tex]

or 64% as a percent.

C. If the wheel is spun 1 time, the probabilty of landing on silver is

[tex]P_3=\dfrac{2}{25}=0.08[/tex]

or 8% as a percent.

If the wheel is spun 100 times, the expected number of landing on silver is

[tex]100\cdot 0.08=8[/tex]

Final answer:

Explaining the probability of landing on different colors on a prize wheel and the expected outcomes in 100 spins.

Explanation:

a) What is the probability of landing on gold?

There is 1 golden section out of a total of 25 sections on the prize wheel.

Probability of landing on gold: 1/25 or 4%

b) If the probability of landing on yellow is 36%, what is the probability of not landing on yellow?

If the probability of landing on yellow is 36%, then the probability of not landing on yellow is 64%.

c) If the wheel is spun 100 times, how many times would you expect to land on silver?

Since there are 2 silver sections on the wheel, the probability of landing on silver is 2/25. Therefore, expected number of times to land on silver in 100 spins is 100 x 2/25 = 8 times.

Answer:

A) 234 feet

B) Area of new parking lot = 28080 square feet

C) The new parking lot will be able to fit 20 more cars than the original parking lot.

Step-by-step explanation:

We are given the following information:

Length of parking lot = 180 feet

Width of parking lot = 120 feet

Number of cars that can be parked = 75

A) Increase in length  = 30%

New length =

[tex]\text{original length} + 30\%(\text{original length})[/tex]

[tex]= 180 + \bigg(\displaystyle\frac{30}{100}\times 180\bigg) = 180 + 54 = 234~feet[/tex]

B) New area =

[tex]\text{New length}\times Breadth\\= 234\times 120 \\= 28080~ square~feet[/tex]

C) Space required by 1 car = 288 square feet

Number of cars we want to fit = 75 + 20 = 95

Area required =

[tex]\text{Number of cars}\times \text{Space occupied by 1 car}[/tex]

[tex]= 95\times 288 = 27360~square~feet[/tex]

Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.

A. This results in a new length of 234 feet.

B. The difference in area is 6480 square feet.

C. The new parking lot's area can only accommodate a fraction of a car more than the original lot's capacity of 75 cars, so it cannot fit 20 more cars.

A. The new length of the parking lot after a 30% increase is calculated by adding 30% of the original length (180 feet) to it.

= 180 * 1.3

= 234 feet

This results in a new length of 234 feet.

B. To find the greater area of the new parking lot compared to the original:

Original area: 120 feet (width) * 180 feet (original length) = 21600 square feet.

New area: 120 feet (width) * 234 feet (new length) = 28080 square feet.

The difference in area: 28080 square feet - 21600 square feet = 6480 square feet.

C. To check if the new parking lot can fit 20 more cars:

New area of the parking lot: 120 feet (width) * 234 feet (new length) = 28080 square feet.

Maximum number of cars in new area: 28080 square feet / 288 square feet per car ≈ 97.5 cars.

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Answer:

Yes

Step-by-step explanation:

1/3 is less than 1 because 1/3 is equal to .3333 and so on

.3333 is less than 1

Answer:

22

Step-by-step explanation:

Since x = 2, we can tell that x is equal to 2.

So this is basically asking 7 times 2 plus 8

7(2) + 8 = ?

14 + 8 = 22

Hope this helps!

Answer:

The answer is below in the photo.

Answer:

We can participate in 10 triathlons.

Step-by-step explanation:

Total cost C to participate in x number of triathlon is given by the expression

C = 90x + 35

If the maximum cost of the annual triathlon is = $1000

Then we can find the maximum number of triathlons by putting C = $1000 in the expression

1000 = 90x + 35

90x = 1000 - 35

90x = 965

x = [tex]\frac{965}{90}[/tex]

x = 10.72

Therefore, we can participate in 10 triathlons.

Answer:

she use altogether flour is [tex]1 \frac{3}{20}[/tex] lb

Step-by-step explanation:

given data

flour to bake a vanilla cake = [tex]\frac{2}{5}[/tex] lb

flour to bake a chocolate cake =  [tex]\frac{3}{4}[/tex] lb

to find out

How much flour did she use altogether

solution

we know here flour use to make cake

so total flour is used = add both flour for vanilla and chocolate cake

total flour is used =  [tex]\frac{2}{5}[/tex] +  [tex]\frac{3}{4}[/tex]

total flour is used =  [tex]\frac{23}{20}[/tex]

she use altogether flour is [tex]1 \frac{3}{20}[/tex] lb

Answer: [tex]\frac{23}{20}\ lb[/tex] or [tex]1\frac{3}{20}\ lb[/tex]

Step-by-step explanation:

For this exercise you need to add fractions.

To bake the vanilla cake, Penny used [tex]\frac{2}{5}\ lb[/tex] of flour and to bake the chocolate cake she used [tex]\frac{3}{4}\ lb[/tex] of flour.

Then, the total flour she used can be found by solving this addition:

[tex]\frac{2}{5}\ lb+\frac{3}{4}\ lb[/tex]

Since the denominators are different, you must find the Least Common Denominator (LCD).

Descompose the denominators into their prime factors and multipy the commons and non-commons with the highest exponent.

Then:

[tex]5=5\\\\4=2*2=2^2[/tex]

[tex]LCD=5*2^2=20[/tex]

So, the sum is:

[tex]\frac{2}{5}+\frac{3}{4}=\frac{4(2)+5(3)}{20}=\frac{23}{20}[/tex]

That improper fraction can be written as a mixed number.

When you divide the numerator 23 by the denominator 20 you get;

Then:

[tex]\frac{23}{20}\ lb=1\frac{3}{20}\ lb[/tex]

Answer:it is option D

Step-by-step explanation:

Answer:

x - 3y = 9

-3y = -x + 9

y = (1/3)x - 3

-1 = (1/3)(3) + b

-1 = 1 + b

b = -2

y = (1/3)x - 2

3y = x - 6

-x + 3y = -6

x - 3y = 6

To find an equation parallel to x - 3y = 9 that passes through the point (3, -1), rearrange the equation to slope-intercept form, determine the slope of the given line, and substitute the slope and coordinates into the point-slope form equation.

To find an equation parallel to x - 3y = 9 that passes through the point (3, -1), we need to determine the slope of the given line and then use it to form the equation of the parallel line.

First, we rearrange the given equation to find the slope-intercept form: y = (1/3)x - 3. We know that the slope of the parallel line will be the same as the slope of the given line, which is 1/3.

Using the point-slope form, we substitute the slope and the coordinates of the given point into the equation: y - (-1) = (1/3)(x - 3). Simplifying, we get the equation of the parallel line as y = (1/3)x + 2.

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Answer:

Simplify the following algebraic expressions.

A) -2x + 5 + 10x - 9

B) 3(x + 7) + 2(-x + 4) + 5x

Simplify the expressions.

A) (2x - 6) / 2

B) (-x - 2) / (x + 2)

C) (5x - 5)/10

Solve for x the following equations.

A) -x = 6

B) 2x - 8 = -x + 4

C) 2x + 1/2 = 2/3

D) x/3 + 2 = 5

E) -5/x = 2

Convert to decimals.

A) 1/5

B) 120%

C) 0.2%

D) 4 8/5

Convert to percent.

A) 3/10

B) 1.4

C) 123.45

D) 2 4/5

Which of these numbers is divisible by 3?

A) 156312

B) 176314

Which of these numbers is divisible by 4?

A) 3432

B) 1257

Which of these numbers is divisible by 6?

A) 1233

B) 3432

Which of these numbers is divisible by 9?

A) 2538

B) 1451

Evaluate 8x + 7 given that x - 3 = 10.

Answer:

Step-by-step explanation:

you have to move the x’s to one side. so the equation would look like

5x = 15

then you have to divide both side of the equation by 5 to get the x by itself which leaves you with

x = 3

Answer is provided in the image attached.

Answer:

Step-by-step explanation:

20 + .15x = 35 + .10x

.05x = 15

x = 300 minutes

Answer:

x = -2, y = -3

Step-by-step explanation:

Multiply eqn1 by the LCM of 1 and 6 i.e coefficients of x

We get:

6x - 54y = 150 (eqn1)

6x - 5y = 3 (eqn2)

- 49y = 147

y = 147

-49

y = -3

Substitute y in eqn2

6x - 5(-3) = 3

6x + 15 = 3

6x = -12

x = -2

Answer:

Add: 3

8

+ 1

2

= 3

8

+ 1 · 4

2 · 4

= 3

8

+ 4

8

= 3 + 4

8

= 7

8

The common denominator you can calculate as the least common multiple of the both denominators - LCM(8, 2) = 8. The fraction result cannot be further simplified by cancelling.

In words - three eighths plus one half = seven eighths.

Answer:7/8

Step-by-step explanation:The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(3/8, 1/2) = 8

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(3/8×1/1)+(1/2×4/4)=?

Complete the multiplication and the equation becomes

3/8+4/8=?

The two fractions now have like denominators so you can add the numerators.

Then:

3/8+4/8=7/8

This fraction cannot be reduced.

Answer:

3/7

Step-by-step explanation:

The ratio is the number of red marbles and the number of blue marbles in a fraction, so the ratio would be 3/7