Express 4 as a fraction.

First off, remember that finding the x-intercepts means setting y equal to zero and solving for the x-values, so this question is really asking you to "Solve 4x2 – 2x – 5 = 0".

Now, let's start the completing-the-square process. To begin, we have the original equation (or, if we had to solve first for "= 0", the "equals zero" form of the equation). In this case, we were asked for the x-intercepts of a quadratic function, which meant that we set the function equal to zero

Answer:

Step-by-step explanation:

Correct choice is D

Answer:

the answer is 24192

Answer: 24192

Step-by-step explanation:

Answer:

Area=LW=(60m)(40m)=2400 m^2

Step-by-step explanation:

The area of the rectangular pen is 2400 square meters.

The region that a rectangle occupies in a two-dimensional space is referred to as the area of a rectangle. The quantity of square units required to entirely fill a rectangle is another way to describe its area. The whole distance encircling a rectangle's outside is referred to as its perimeter.

Given, A rectangular animal pen will be built using 200 meters of fencing. If one side of the fence is 60 meters. Hence,

Parameter of rectangle = 200

2(length + width ) = 200

given length of the pen is 60 meters

2(60 + width) = 200

width = 100- 60 = 40

Area of the rectangle = length * width = 60* 40 = 2400

Therefore, 2400 square meters will be the area of the given rectangular pen.

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Answer:

ok I think it's A I'm taking the quiz :)

Step-by-step explanation:

From the table, we see that:

• Year 0 has a population of 10,

• Year 2 has a population of 20.

So after two years, the population of fish is doubled.

1) By year 4, we will have double the population of year 2, so the population will be 2*20 = 40.

2) To function that describes the growth of the population is:

Where P_0 is the initial population and r is the growth factor.

We know that after two years, the population of fish is doubled:

Using the formula above evaluated in t + 2, we have:

Equalling the last two equations, we have:

Solving for r the last equation, we have:

So the growth factor is r = √2.

Answer:

1. 40

2. √2

Answer:

15,659,568

Step-by-step explanation:

To calculate the expression 2308208 * 12 - 12038928, we can follow the order of operations (PEMDAS/BODMAS):

1. Multiply: 2308208 * 12 = 27698496

2. Subtract: 27698496 - 12038928 = 15659568

Therefore, 2308208 * 12 - 12038928 equals 15,659,568.

The probability of rolling a specific number is 1/6 or approximately 0.1667.

When rolling a fair number cube with faces numbered 1 through 6, each face has an equal chance of landing face-up. This means the probability of rolling any specific number is 1 out of the total number of faces, which is 6. Therefore, the probability of rolling a specific number is 1/6 or approximately 0.1667.

The dot on the number line represents the probability of an event occurring when rolling the number cube. To determine what this event could be, consider the possible outcomes when rolling the cube and compare their probabilities to the dot's position on the number line.

For example, if the dot is located at 1/6 on the number line, this could represent the probability of rolling a single specific number, such as rolling a 3. If the dot is located at 1/2 or 0.5, it could represent the probability of rolling an even number (2, 4, or 6) since there are three even numbers out of the six total faces, making the probability 3/6 or 1/2.

In summary, the dot on the number line represents the probability of an event occurring when rolling a fair number cube. To identify the event, compare the dot's position on the number line with the probabilities of different outcomes resulting from rolling the cube.

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On solving the provided questions, we can say that Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

he diameter of the ball bearings varies according to a distribution that is approximately Normal

mean 11.5 mm and standard deviation 0.05 mm

the probability that the difference in the diameters of the two ball bearings is less than 0.06 mm

Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

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Answer:

Step-by-step explanation:

Mean = (11.4 + 13.9 + 11.2 + 14.5 + 15.2 + 8.1 + 12.4 + 8.6 + 10.5 + 17.1 + 9.8 + 15.9)/12 = 12.4

Standard deviation = √(summation(x - mean)²/n

n = 12

Summation(x - mean)² = (11.4 - 12.4)^2 + (13.9 - 12.4)^2 + (11.2 - 12.4)^2+ (14.5 - 12.4)^2 + (15.2 - 12.4)^2 + (8.1 - 12.4)^2 + (12.4 - 12.4)^2 + (8.6 - 12.4)^2 + (10.5 - 12.4)^2 + (17.1 - 12.4)^2 + (9.8 - 12.4)^2 + (15.1 - 12.4)^2 = 89.62

Standard deviation = √(89.62/13) = 2.7

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

µ ≤ 15

For the alternative hypothesis,

µ > 15

This is a right tailed test

b) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 12,

Degrees of freedom, df = n - 1 = 12 - 1 = 11

t = (x - µ)/(s/√n)

Where

x = sample mean = 12.4

µ = population mean = 15

s = samples standard deviation = 2.7

t = (12.4 - 15)/(2.7/√12) = - 3.34

We would determine the p value using the t test calculator. It becomes

p = 0.0034

c) Assuming level of significance = 0.05.

Since alpha, 0.05 > than the p value, 0.0034, then we would reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the water from this source does meets the EPA standard. They are higher than 15ppb

Using the t-distribution, we have that:

a)

The null hypothesis is: \(H_0: \mu \geq 15\)

The alternative hypothesis is: \(H_1: \mu < 15\)

b) The p-value is of 0.0051.

c) Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.

Item a:

At the null hypothesis, it is tested if the mean is of at least 15 ppb, that is:

\(H_0: \mu \geq 15\)

At the alternative hypothesis, it is tested if the mean is of less than 15 ppb, that is:

\(H_1: \mu < 15\)

Item b:

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

In this problem, we have that \(\mu = 15, n = 12\). Additionally, using a calculator, the other parameters are: \(\overline{x} = 12.38, s = 2.93\)

Hence, the value of the test statistic is:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{12.38 - 15}{\frac{2.93}{\sqrt{12}}}\)

\(t = -3.1\)

The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with t = -3.1 and 12 - 1 = 11 df.

Item c:

Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.

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There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

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Answer:

answer below

Step-by-step explanation:

C=5/9(F--32)

9C/5=F--32

F=9C/5 +32

When C=30

F=(9*30/5)+32=9*6+32=54+32=86

F=86

so the answer is 86

hope this helps ^^

Answer:

What is the real increase if VAT increases from 10% to 14%?

Step-by-step explanation:

What is the real increase if VAT increases from 10% to 14%?

Answer:

Total revenue = 13.5 + 9 = $22.5

Step-by-step explanation:

The toll charges $1.00 for passenger cars and $2.25 for other vehicles. During daytime hours  60% of all the vehicles are passenger vehicles.

A particular daytime period 15 vehicle crossed the bridge. Recall that during daytime period, 60% of all the vehicles are passenger vehicles . Therefore,

Passenger vehicles = 60% of 15

Passenger vehicles = 60/100 × 15

Passenger vehicles = 900/100

Passenger vehicles = 9

9 of the vehicles are passenger vehicle and the charges for passenger cars is $1.00. other vehicle is $2.25.

revenue for passenger cars = 1 × 9 = $9

revenue for other vehicles = 2.25 × 6 = $13.5

Total revenue = 13.5 + 9 = $22.5

The dimensions of the box if it is to use the minimum possible amount of metal are,

⇒ 2.714 m, 2.714 m, 1.358 m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A container with an open top is to have 10 m³ capacity.

Now,

Let the dimensions are x, y and z.

Since, Volume of box = 10 m³

Hence, We get;

⇒ xyz = 10

⇒ z = 10/xy

Since, A container is open in top.

Hence, The surface area = 2xz + 2yz + xy

Substitute z = 10/xy;

⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy

          = 20/y + 20/x + xy

For minimum metal;

⇒ d (S.A)/ dx = 0

⇒ - 20/x² + y = 0

⇒ y = 20/x²  ..(i)

And, d (S.A) / dy = 0

⇒ - 20/y² + x = 0

⇒ x = 20/y²   ..(ii)

Divide equation (i) and ((ii);

⇒ x = y

Hence, We get;

⇒ xyz = 10

⇒ x³ = 10

⇒ x = 2.714

And, y = 2.714

So, The value of z is,

⇒ z = 10/xy

⇒ z = 10 / 2.714×2.714

⇒ z = 1.358 m

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Answer:

5/6

Step-by-step explanation:

12/3 × 1/2 = 5/6

hope it helps

please mark Brainliest

Answer:i dont know to do this stuff but i think you have to divide i think ???

Step-by-step explanation:

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

The inequality that represents p, the number of people the theater can seat is p ≤ 25

From the question, we have the following parameters that can be used in our computation:

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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Answer:

Option D: 8.19 inches

Step-by-step explanation:

i hope this helps..have a great day! :)

Answer:

7x - 6y = 16

y = (-5)

using substitution method

7x - 6(-5) = 16

7x +30 = 16

7x = 16 - 30

7x = 14

x = 14/7

x= 2

Answer:

(1,5) (7,13) (10,17) (7,13)

Step-by-step explanation:

1 4  7  10  13

5 9 13 17 21

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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7 groups of 2/7 is equivalent to the whole, which is represented by the number 2.

When we have 7 groups of 2/7, we are essentially multiplying the fraction 2/7 by the whole number 7. To perform this operation, we can use the following formula:

a/b × c/d = ac/bd

where a, b, c, and d are any numbers, and a/b and c/d are two fractions.

In our case, a is 2, b is 7, c is 7, and d is 1. This is because we want to multiply 2/7 by 7 to get 7 groups of 2/7. Therefore, we can substitute these values into the formula:

2/7 × 7/1 = (2 × 7) / (7 × 1) = 14/7

The result is a fraction 14/7, which can be simplified to 2. This means that 7 groups of 2/7 is equal to 2. To simplify this further, we can say that if we divide a whole into 7 equal parts, each part is 2/7. If we have 7 of these parts, we have the whole.

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We get the following answers;

(a) The necessary histogram has been created and is supplied below.

(b) According to the data, it is indeed dangerous to drive close to home. Because 23% and 29% of accidents occur within 1 to 5 miles of home, respectively.

Step 1: in 2001, progressive insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. the data are summarized in the table.

Step 2:

Table :

Miles from home          % of accidents      Cumulative

Less than 1                               23                        23

1 to 5                                         29                        52

6 to 10                                       17                         69

11 to 15                                       8                          77

16 to 20                                     6                         83

over 20                                     17                        100

(a) the required histogram is made and attached below.

(b) Yes, the data indicates that driving near home is particularly dangerous. Because, less than , 1 to 5 miles from home 23%, 29% of accidents.

Hence we get the required answers.

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Answer:

Step-by-step explanation:

Les opinions des 450 élèves d'un lycée quant à savoir s'ils soutiennent le candidat A à la présidence du corps étudiant sont présentées ci-dessous. Masquez et mélangez toutes les valeurs. Prenez un échantillon aléatoire de 25 valeurs de la population. Sur la base de cet échantillon, trouvez la proportion de l'échantillon et utilisez cette valeur pour créer un intervalle de confiance à 95 % pour la véritable proportion de la population qui soutient le candidat A, en arrondissant au millième le plus proche.

Échantillon Oui : 19 Échantillon N° : 6 Échantillons : 25

Answer:

x = 7deg

Step-by-step explanation:

7x + 10 + 15x + 16 = 180 (angles adjacent to each other in a //polygon are supplementary)

22x = 154

x = 7deg

This is a question on polygons and angles. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

With two sections rectangular and triangular, volume of the building is 39.105 m³.

What exactly is a rectangle?

A rectangle is a two-dimensional geometric shape that has four sides and four angles. It is a type of quadrilateral with opposite sides that are parallel and congruent (having the same length). The opposite angles of a rectangle are also congruent, each measuring 90 degrees.

Rectangles are often described using the length of their sides. The two longer sides of a rectangle are called the length, and the two shorter sides are called the width. The area of a rectangle is calculated by multiplying the length by the width, and the perimeter is calculated by adding together the lengths of all four sides.

Now,

To calculate the volume of the stone outbuilding, we need to find the volume of each individual section and add them together.

The volume of the rectangular section of the building is:

V1 = length x width x height

V1 = 3.5m x 2.2m x 2.5m

V1 = 19.25 cubic meters

The volume of the triangular section of the roof is:

V2 = (1/2) x base x height x length

V2 = (1/2) x 4.3m x 2.6m x 3.5m

V2 = 19.855 cubic meters

Therefore, the total volume of the stone outbuilding is:

V total = V1 + V2

V total = 19.25 + 19.855

V total = 39.105 cubic meters

Therefore, the volume of the stone-out building is 39.105 m³.

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Right question:- A stone outbuilding is 4. 3 metres high, 3. 5 metres wide and 2. 2 metres deep. The slope of its roof is 2. 6 m long, whilst its side walls are 2. 5 metres high. Calculate its volume?

Answer:

The answer to this question is

Angle at C is 35

Angle at D is 81

Angle at E is 64

because y=6

Answer:

∠C = 35

∠D = 81

∠DEC = 64

Step-by-step explanation:

Exterior angle theorem - An exterior angle of a triangle is equal to the opposite interior angles of a triangle.

∠DEF is an exterior angle of ΔCED

∠DCE and ∠ CDE are opposite interior angles of ∠DEF

That being said we know that ∠C + ∠D = ∠DEF

We will use this as our equation

* plug in the information we are given about each angle into the equation *

5y + 5 + 13y + 3 = 116

Now we solve for y using basic algebra

step 1 combine like terms

5y + 13y = 18y

5 + 3 = 8

now we have  18y + 8 = 116

step 2 subtract 8 from each side

8 - 8 cancels out

116 - 8 = 108

now we have 18y = 108

step 3 divide each side by 18

18y / 18 cancels out

108 / 18 = 6

we're left with y = 6

Now to find the measures of ∠C and ∠ D

To find the measure of each we replace " y " in the given expression with 6

For ∠C

5y + 5

* replace y with 6 *

5(6) + 5

5(6) = 30

30 + 5 = 35

Hence ∠C = 35

For ∠D

13y + 3

* replace y with 6 *

13(6) + 3

13(6) = 78

78 + 3 = 81

Hence ∠D = 81

Finally we want to find ∠DEC

We can do this by using the triangle angle rule which states that the angles of a triangle should add up to equal 180

so to find the missing angle we subtract the given angles ( 81 and 35 ) from 180

so ∠DEC = 180 - 81 - 35

180 - 81 - 35 = 64

Hence ∠DEC = 64

Answer:

its the one you have selected

Step-by-step explanation:

you have to ask something about your assignment

and its the one you have selected

have a nice day!

Answer:

Rhonda earned: $72

Anne earned: $52

Step-by-step explanation:

divide $124 by 2 = 62

subtract 10 from 62 = $52 (Anne)

add 10 to 62 = $72 (Rhonda)

Answer:

-0.33333333333 in other word it o.3 with line over 3

Step-by-step explanation: