Write 14 7/8% as a decimal

Answer:

\({ \rm{ {a}^{ \frac{b}{c} } \: \dashrightarrow \: ( {a}^{b}) {}^{ \frac{1}{c} } }} \\ \\ { \boxed{ \rm{ \boxed{} \: \: \sqrt[c]{ {a}^{b} } }}} \\ \)

9 gallons + 7 gallons = 16 gallons

1 qt + 2qt = 3 qts

Total = 16 gallons and 3 qts.

The Grassgreen required by the company to mix with 15 kg of Britegreen is 22.5 kg.

The price of Britegreen grass seed =  £18 per kilogram.

The price of Grassgreen grass seed = £21 per kilogram.

Let the weight of Grassgreen mixed be 'x'.

The weight of Britegreen mixed be 'y' = 15 Kg.

The ratio of of the weight s given as Britegreen: Grassgreen = 2:3.

Thus,

y/x = 2/3

Cross multiplying;

3y = 2x

Or,

x = 3y/2

Put y = 15

x = (3×15)/2

x = 22.5

The the weight of the Grassgreen be mixed with the 15 kg of Britegreen is 22.5 kg.

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Answer:

f and g share no roots in common

Step-by-step explanation:

The roots of \(f(x)=0\) are \(x=\pm 3\).

From the graph, the roots of \(g(x)=0\) are where the graph of \(g(x)\) intersects the \(x\) axis, which are at \(x=2, 10\).

Answer:

the number is 18.

Step-by-step explanation:

9×2 =18

18-10= 8

The value of g(4) is 7 when given function is g(x)= 4x-9 .

By considering the given function

g(x)= 4x-9

g(4)=4(4)-9

g(4)=16-9

g(4)=7

A function in mathematics that goes from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are referred to as the function's domain and codomain, respectively.

a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are everywhere in mathematics, and they are essential for constructing physical relationships in the sciences.

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Step-by-step explanation:

a² + b²

difference of two square

= (a + b)(a - b)

Answer:

see explanation

Step-by-step explanation:

(a + b)(a - b)

each term in the second factor is multiplied by each term in the first factor, that is

a(a - b) + b(a - b) ← distribute parenthesis

= a² - ab + ab - b² ← collect like terms

= a² - b²

Answer:

B) -2

Step-by-step explanation:

The slope of the line can be solved by using the following equation:

slope \((m) = \frac{y_2 - y_1}{x_2 - x_1}\)

Let: \((x_1, y_1) = (0 , 4)\\(x_2 , y_2) = (-1 , 6)\)

Plug in the corresponding numbers to the corresponding variables:

\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (4)}{-1 - (0)}\)

\(m = \frac{6-4}{-1 - 0} = \frac{2}{-1}\)

m = -2 is your answer.

~

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Answer:

The answer is B

-2

Step-by-step explanation:

slope =rise/run

\(m = \frac{y(2) - y(1)}{x(2) - x(1)} \)

\(m = \frac{6 - 4}{ - 1 - 0} \)

\(m = \frac{2}{ - 1} \)

\(m = - 2\)

Answer:

27/2

Step-by-step explanation:

x=1 y=9/2

x=3 y=27/2

Answer:

27/2

Step-by-step explanation:

\(f(g(13)) = f( \alpha ) \\ where \: \alpha = g(13)\)

As shown in the output of g when we want to input 13 is shown in the second figure.

\( \alpha = g(13 )= 16\)

Now we want to solve for f(g(13)),now that we know what g(13) is

\(f(g(13)) = f( \alpha ) = f(16) = 32\)

Answer:

C=32

Step-by-step explanation:

This mapping is both one to one mapping and onto mapping

f(g(13))=f(ã)

since we know that g(13),we proceed to the codomain of g which is g(16)

That will be

f(16)=32

4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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Answer:

A)

Step-by-step explanation:

A hypothesis is a put forth explanation of a phenomenon (plural: hypotheses). Therefore, p-value given is 0.0062.

A hypothesis is a put forth explanation of a phenomenon (plural: hypotheses). A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.

H:p<=0.8

Ha: p>0.8

alpha=0.01 P{reject H:H is true}

critical value z>2.326

z=(0.9-0.8)/sqrt (0.8*0.2/100); sqrt of 0.0016=.04

z=(0.1/.04)=2.5

probability z> 2.5 is 0.0062

check with one sample proportion test on calculator, z=2.5

Reject H

p-value given is 0.0062

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The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.

Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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a) We know that 13 cities had soccer and football, 13 had soccer and volleyball, and 7 had all three sports. Therefore, the number of cities that had only 5 soccer.

b)  34 cities had either a soccer team or a football team.

c)27 cities had either a soccer team or a football team, but not a volleyball team.

What is set theory?

(a) To find the number of cities that had only a soccer team, we need to subtract the cities that had soccer and at least one other sport from the total number of cities that had soccer.

From the given information, we know that 13 cities had soccer and football, 13 had soccer and volleyball, and 7 had all three sports. Therefore, the number of cities that had only soccer is:

24 (total cities with soccer) - 13 (cities with soccer and football) - 13 (cities with soccer and volleyball) + 7 (cities with all three sports) = 5

So, 5 cities had only a soccer team.

(b) To find the number of cities that had soccer or football, we need to add the number of cities that had soccer to the number of cities that had football and then subtract the cities that had both soccer and football (which were counted twice).

From the given information, we know that 24 cities had soccer, 23 had football, and 13 had both. Therefore, the number of cities that had soccer or football is:

24 (cities with soccer) + 23 (cities with football) - 13 (cities with both) = 34

So, 34 cities had either a soccer team or a football team.

(c) To find the number of cities that had soccer or football, but not volleyball, we need to subtract the cities that had all three sports from the total number of cities that had soccer or football (which we calculated in part b).

From the given information, we know that 7 cities had all three sports. Therefore, the number of cities that had soccer or football, but not volleyball, is:

34 (cities with soccer or football) - 7 (cities with all three sports) = 27

So, 27 cities had either a soccer team or a football team, but not a volleyball team.

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Answer:

1/10

Step-by-step explanation:

because if you share/divide 1/5 by 5 then every dog will get 1/10

Answer:

x = 0, 2, -3

Step-by-step explanation:

these are the points from the function f(x) that we are certain that the y  value is -1. if you look at the graph at each of these induvidual points y is -1

Answer:43 8/15

Step-by-step explanation:45-2/3 is 44 1/5 then subtract 44 8/15 by 4/5 and you get 43 8/15

The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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Answer:

C.

Step-by-step explanation:

Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

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The prove that the modus ponens is a valid argument form in correct order is

The complete question is given below:

1. ~p V -(p = q) Vq = (Tp Vq) v-(Tp V q)

2. Since the disjunction of an expression and its negation is always true, Zp V q) v-(-p V q) is a tautology: This completes the proof:

3. ~(p ^ (p + 9)) Vq =-pV (p + 9) Vq 10

4. Using the rule p 7 q =7p V 4, we rewrite the given expression as 12

5. ~(p ^ (p = 4) Vq =-pv-Wpv 9)Vq

6. To prove the validity of the modus ponens, we need to show that (p 5 9) 5 4 is a tautology:

7. We now reorder and re-associate the terms of the last expression by using the associative and commutative laws and apply the rule p v q = 7pV q again: N

8. To prove the validity of the modus ponens; we need to show that (p ^ (p 7 74 is a tautology:

9. (p v q) - 4=-pv 9Vq

10. Using the rule p 4 q =7p ^ q, we rewrite the given expression as 13

11. By the domination law; the last expression is always true: This completes the proof: 11

12 Zp V-(p - 9) Vq = (~p V 9) ^ -(-p V9)

13. We now use one of the rules of De Morgan:

14. (p ^ (p = 9)) - q =-(p ^ (p = 9)) V q

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The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

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

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

I believe the answer is 3 1/8

Step-by-step explanation:

Since he uses 1 1/4 packages just to make 10, we can start with him making the 20. That would mean he uses 2 1/2 packages. Now all we have left is the 5 in 25. 5 is half of 10 and since you use 1 1/4 to make 10 bracelets, use half of it to make 5. Add up all the package use and you get 3 1/8. This was kinda rushed so I'm not 100% sure, but I'm like 95% sure. Hope this helps!

3¹/₈ packages of beads are required to make 25 bracelets

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Here it is given that :

Darnell uses 1 1/4 packages of beads to make 10 bracelets that is :

1 ¹/₄ = 5/4 packages of beads requires to make = 10 bracelets

Now, divide both side by 10 we get :

to make 1 bracelets = 5/40 = 1/8  packages of beads are required

Now, to find the numbers  packages of beads to make 25 bracelets multiply both side by 25 :

to make 25 bracelets =  25/8  = 3¹/₈ packages of beads are required.

Therefore, 3¹/₈ packages of beads are required to make 25 bracelets

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The price of the bed after mark up is $475.00

Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.

The first discount given is 25% , therefore the price of the bed before mark up is

25/100 × 800

= 25×8

= 200

the price before mark up = 800-200 = $600

Another 25% is given after the first sale, there the price of the bed after mark up is

25/100 × 600

=$ 125

price after markup = 600-125

= $475.00

therefore the price of the bed after markup is $475.00

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Answers:

90 ounces of solution A.

60 ounces of solution B.

====================================================

Explanation:

x = amount of solution A

150-x = amount of solution B

Each amount is in ounces and they add to 150 ounces.

Solution A is 35% salt, so we get 0.35x ounces of pure salt from solution A.

Solution B is 60% salt, so we get 0.60*(150-x) = 90-0.60x ounces of pure salt from solution B.

We want 150 ounces of 45% salt solution, which means we want 150*0.45 =  67.5 ounces of pure salt when everything is mixed.

Here's a table showing this info

\(\begin{array}{|c|c|c|} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 0.60(150-\text{x}) = 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 150*0.45 = 67.5 \\\cline{1-3}\end{array}\)

Cleaning up the table a bit shows

\(\begin{array}{|c|c|c|} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 67.5 \\\cline{1-3}\end{array}\)

Focus on the "pure salt" column.

We want the 0.35x and 90-0.60x to add to 67.5

So,

0.35x+(90-0.60x) = 67.5

90-0.25x = 67.5

-0.25x = 67.5-90

-0.25x = -22.5

x = -22.5/(-0.25)

x = 90

She must use 90 ounces of solution A.

150-x = 150-90 = 60 ounces of solution B must be used as well.

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

Check:

35% of 90 = 0.35*90 = 31.5 ounces of pure salt comes from solution A.

60% of 60 = 0.60*60 = 36 ounces of pure salt comes from solution B.

31.5+36 = 67.5 ounces of pure salt in total, which matches with the value mentioned earlier. The answers are confirmed.

Answer: the answer is C

Step-by-step explanation:

On the map, a trail is 5 1/4 inches long, its actual length is 3 and 1/2 miles. Option C is correct.

As given that, A trail map has a scale of 3 inches to 2 miles. To determine the actual length of the measure 5 1 / 4 inches in miles.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
3 inches = 2 miles
1 inches = 2 / 3 miles
multiply both side by 5 1/4 = 21 / 4
21 / 4 inches = 21 / 4 * 2 / 3 miles
21 / 4 inches = 3 1/2 miles

Thus, on the map, a trail is 5 1/4 inches long, and its actual length is 3 and 1/2 miles. Option C is correct.

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In order to determine the distance between numbers -8 and -2, you calculate the difference between the given number, just as follow:

-2 - (-8) = -2 + 8 = 6

Then, the distance between the given numbers is 6.

On a number line you obtain the following result: