A box of cereal states that there are
78 calories in a
3
4
​-cup serving. What is the unit rate for calories per​ cup? How many calories are there in
4 cups of the​ cereal?

The resulting coordinate of △ D'E'F' is translated by the vector is

(-1, -2),  (3,-4), and (1, -7)

Given the vertices of ∆DEF are D(2,5), E(6,3), and F(4,0).

we are asked to graph ∆DEF and its image when you translate ∆DEF using the vector (-3,-7)​.

If the coordinate of the vertices is translated by the vector (-3, -7), the resulting coordinates of △ D'E'F' will be expressed as:

D'= (2-3, 5 - 7) = (-1,-2)

E' = (6 - 3, 3 - 7) = (3, -4)

F' = (4 -3 , 0 - 7) = (1, -7)

Hence we get the required coordinates of the translated image.

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The probability that one or more of them tests negative is 0.85.

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

If Marv and Patricia will each take a Covid test, then the events that will occur are : both will test positive, both will test negative, or one of them will test negative.

Based on the given information, the probability that both will test positive is 0.15. Subtract it from 1 to and get the probability that one or more of them tests negative.

probability = 1 - 0.15

probability = 0.85

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Each child will receive the 1.1 cup of milk.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that a container of milk contains 8 cups of milk. if paul sets aside [tex]1\dfrac{2}{5}[/tex] cups of milk for use in a recipe , then we get the leftover;

8  -  [tex]1\frac{2}{5}[/tex] = 8 -  7/5

= 40- 7/5

= 33/5

= 6.6

The the rest cups of milk = 6.6

Then the rest evenly among his three children 6.6/3 = 1.1

Hence, Each child will receive the 1.1 cup of milk.

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4.8% of voters with annual incomes over $50,000 will be polled, or at least 1,450 of them when an opinion poll of 4,000 (randomly selected) voters is con.ducted

What is probabilty ?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

We have,

n = 4000

p = 0.35 , q=1-p=0.65

= E(X) = np= 4000 (0.35) 600 1400

6 = SE(X) = √npq √ 4000 (0-35)(0.65) = 30.1662

Consider

P(X[tex]\geq[/tex]1450) = p 7

X-U

1450 1400

30.1662

=P(z>1,66)

=0.048457

from standard normal table,

Hence, 4.845% chance that 1,450 or more of the voters with annual incomes above $50,000 will be polled

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You have the following vertices of a triangle:

A(1,1)

B(4,1)

C(4,5)

For the translation four untis to the right, consider this kind of translation means that it is necessary to sum 4 units to the x-coordinate:

A(1,1) => A'(1+4,1) = A'(5,1)

B(4,1) => B'(8,1)

C(4,5) => C'(8,5)

Next, a translation three units up is done by adding 3 units to the y-coordinate of points A', B' and C':

A'(5,1) => A''(5,1+3) = A''(5,4)

B'(8,1) => B''(8,4)

C'(8,5) => C''(8,8)

Next, a reflection around y=-1 consists in subtracting to the y-coordinate units equivalent to the vertical distance to the line y =-1, just as follow:

for the point A''(5,4) you can notice that the vertical distance of the y-coordinate, which is 4, to the line y=-1 is 5 units, then, it is necessary to subtract 5 units to such line:

A''(5,4) => A'''(5,-1-5)=A'''(5,-6)

for the point B''(8,4), the distance is again 5 units, then, you have:

B''(8,4) => B'''(8,-1-5) = B'''(8,-6)

for the point C''(8,8) the distance from y-coordinate y=8 to the line y=-1 is 9 units, then, yu subtract 9 units to -1:

C''(8,8) => C'''(8,-1-9) = C'''(8,-10)

Hence, the final points are:

A'''(5,6)

B'''(8,-6)

C'''(8,-10)

The formula to calculate the missing arc is,

where,

Therefore,

Hence, the answer is

A set of parallel lines and a set of perpendicular lines are: BF║CG, AD⊥BF.

Parallel lines are straight lines that are of equal distance at every point away from each other, and therefore, do not intersect each other at any point. The sign "║" is used to indicate that two lines are parallel lines.

Lines that are said to be perpendicular lines are lines that intersect each other at right angle or 90 degrees. That is, at the point of their intersection, a right angle is formed which is 90 degrees. The sign "⊥" is used to indicate that two lines are perpendicular lines.

In the image given, lines BF and CG do not intersect at any point and they are of equal distance away from each other at every point, therefore, CG and BF are perpendicular lines.

Also, we can see that a right angle is formed at the point of intersection of lines AD and BF, therefore AD and BF are perpendicular lines.

Thus, we can state that: BF║CG, AD⊥BF.

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Answer:

1.95 hours or 1 hour and 57 minutes.

Step-by-step explanation:

You can read the problem as 13% of the battery. "Of" is a keyword that means to multiply.

The battery lasts 15 hours, so multiply by 13%. You need to change 13% to a decimal first by dividing it by 100, or moving the decimal left two places.

13% = 0.13

Now solve.

0.13 × 15 = 1.95

If you need to convert the 0.95 to minutes, multiply it by 60 since there are 60 minutes in an hour.

0.95 x 60 = 57 minutes.

Answer:

1. 39, 46

2. 180

Step-by-step explanation:

1. count up by 7

2. not sure..

The perimeter of the regular polygon is 108 units.

A regular polygon is a polygon that has all its sides equal to each other.

Therefore,

5(x + 2) = 7x + 4

5x + 10 = 7x + 4

5x - 7x = 4 - 10

-3x  = -6

x = -6 / -3

x = 2

The perimeter of a regular polygon is the sum of the whole sides of the polygon.

Therefore,

each side of the regular polygon = 7(2) + 4

each side of the regular polygon = 14 + 4

each side of the regular polygon = 18

Hence the regular polygon has 6 sides

perimeter of the regular polygon = 18  × 6

perimeter of the regular polygon = 108 units

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Answer:

X=11

Step-by-step explanation:

Answer:

x=18

Step-by-step explanation:

Because, [tex](8*18+14)=(9*18-4)[/tex] is true

Answer: The answer is 0.

X = 0 when evaluated.

Step-by-step explanation:

The value of x from the given linear equation is equivalent to 1.1

Linear equations are equation that has a leading degree of 1. An example of a linear equation is y = mx + b

Given the equation

19+2 In x=25

2lnx = 25 - 19

Simplify to have:

2lnx = 6

lnx = 6/2

lnx = 3

Take the exponent of both sides

e^lnx = ln3

x = ln3

Hence the approximate solution to the given linear equation is 1.1.

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The resulting value for the quotient of 21 and a equals 30 is 7/10.

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three.

Latin's "how many times" is the meaning of the word "quotient." That is really logical. For instance, the quotient of a and b is a/b

Given the statement "the quotient of 21 and a equals 30", this can be written mathematically as;

21/a = 30

Cross multiply

30a = 21

Divide both sides by 30

30a/30 = 21/30

a = 21/30

a = 7/10

Hence the value of a from the equivalent expression is 7/10.

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The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²

Missing data from the problem:

radius of the barrel = 0.4 meters

height of the barrel = 1.2 meters

The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:

A = 2. πr² + 2. πr.h

Where:

r = radius

h = height

Plug the parameters into the formula:

A = 2. π(0.4)² + 2. π(0.4).(1.2)

A = 13 m²

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Answer:

2a + b = 180
 a + b = 118

a = 64, b = 56

Step-by-step explanation:

If you look at the triangle on the top right of the diagonal, there are 3 angles a, a and b. Since the 3 angles of a triangle add up to 180°

      a + a + b = 180

=>   2a + b = 180.......(1)

We are given that the largest angle is 118°

The largest angle of the parallelogram is a + b. Remember that opposite angles of a parallelogram are equal and the sum of the angles add up to 360

Therefore a + b = 118 ....(2)

Given equations (1) and (2), subtract (1) from (2):

Eq (1) - Eq(2) :

2a + b - (a + b) = 180 - 118

a = 62

Substitute for a in equation (2) to get

a + b = 118

62 + b = 118

b = 118 - 62 = 56

So the two angles are a = 64° and b = 56°

Answer:

a = 62, b = 56

Step-by-step explanation:

given the largest angle is 118° , then

a + b = 118 ( subtract b from both sides )

a = 118 - b → (1)

the sum of the interior angles of a quadrilateral = 360°

the angle adjacent to a is b ( alternate angles ) , then

a + b + a + a + b + a = 360

4a + 2b = 360 → (2)

substitute a = 118 - b into (2)

4(118 - b) + 2b = 360

472 - 4b + 2b = 360

472 - 2b = 360 ( subtract 472 from both sides )

- 2b = - 112 ( divide both sides by - 2 )

b = 56

substitute b = 56 into (1)

a = 118 - 56 = 62

a = 62 and b = 56

Answer:

769 and 858

Step-by-step explanation:

Every hour, the distance between the two planes increases by 2x + 89

2 hours = 4x + 178

3254 = 4x + 178

4x = 3076

x = 769

4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is

4/36=1/9

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

If four people use all three facilities,

then 16 - 4 = 12 of them use the gym and the track but not the pool, and 9 - 4 = 5 of them use the pool and the track but not the gym.

The pool and gym are used by 19 - 4 = 15 individuals, however the track is not used.

4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is

4/36=1/9

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In terms of the calculation, the answer is 39/4 in improper fraction.

An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.

A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.

The given equation is [tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] .

Taking 4 as LCM from the above equation.

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13/4) + (13/2)

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13+26)/4

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = 39/4

Now, since the solution must be proffered in an improper fraction.

Therefore, the obtained improper fraction is 39/4.

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Answer:

Whats the question?

Answer: f(7) = 52

Step-by-step explanation:

x = 7, so you would substitute x for 7

f(7) = 6(7) + 10

f(7) = 42 + 10

f(7) = 52

Hope this helps!

SINCE A OF A RECTANGLE IS =L×B

[tex] = (12x - 6)(14 \frac{1}{6} ) \\ = (12x - 6)( \frac{25}{6} ) \\ = \frac{25}{6} (12x) + \frac{25}{6} ( - 6) \\ = 50x - 25[/tex]

THE SIMPLIFIED AREA IS =50x-25

Answer:

y = (1/4)x - 5

Step-by-step explanation:

We'll look for an equation having the form y=mx+b, where m is the slope and b is the y-intercept, the value of y when x=0.

We are told the slope, m, is (1/4):

  y = (1/4)x+ b

We need to find a value of b such that it forces the line to go through point (8,-3).  Enter that point in the equation:

  y = (1/4)x + b

  -3 = (1/4)(8) + b    for (8,-3)

   -3 = 2 + b

b = -5

The equation is y = (1/4)x - 5

See attached graph.

Check the picture below.

[tex]tan(x )=\cfrac{\stackrel{opposite}{13}}{\underset{adjacent}{6}}\implies tan^{-1}[tan(x)]~~ = ~~tan^{-1}\left( \cfrac{13}{6} \right) \\\\\\ x~~ = ~~tan^{-1}\left( \cfrac{13}{6} \right)\implies x\approx 65^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

a. Yes

Step-by-step explanation:

If you plug the numbers in, 1 is x and -1 is y. The equation would look something like this:

4-5=-1

Now, do 4-5

4-5=-1

-1=-1

The answer would be a, yes.

Hope this helps! :D

The foot will be moving at a rate of 2.373 ft/s away from the wall when the top is 13 feet above the ground.

From the question, we have the following;

Hypotenuse=17 foot

Height(y)=13 feet

Base(x)=(17^2-13^2)^1/2

        =120^1/2 or sqrt(120)

The ladder against the wall is a right angle triangle, so we have:

x^2+y^2=17^2

x^2+y^2=289

Top slips down at 2ft/s

dy/dt=-2 ft/s, where height (y)=13ft

The foot will be moving horizontally(x), along the x axis, to find how fast the foot will be moving, we find dx/dt

Now, we take the derivative with respect to time:

=x^2+y^2=17^2

=2x(dx/dt)+2y(dy/dt)=0

Substitute the known values, y=13, x=sqrt(120), z=17, dy/dt=-2 ft/s

2(sqrt(120))(dx/dt)+2(13)(-2)=0

2(sqrt(120))(dx/dt)-52=0

We solve for dx/dt:

dx/dt=52/(2sqrt(120))

dx/dt=52/21.9089

dx/dt=2.373 ft/s

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Using the properties of equality, the value for m in the equation is: m = pV.

For any given equation, to solve for a variable in the equation, we have to isolate the variable to one side of the equation in order to determine its value. To do this, several properties of equality need to be applied to isolate the variable to one side of the given equation.

Given the equation, p = m/V, we need to isolate the variable m to one side of the equation in order to solve for m.

p = m/V

Multiply both sides of the equation by V

p × V = m/V × V [multiplication property of equality]

Simplify the equation:

pV = m

m = pV

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Answer:

A) y = 23°

B) ∠A = 67°, ∠C = 113°, ∠D = 113°

Step-by-step explanation:

Hello!

Angle A and B are vertical angles, meaning they are equal in measure. We can solve for y by setting the two equations equal to each other.

Vertical angles are the opposite angles formed by the intersection of 2 lines.

Supplementary angles are angles that add up to 180°.

The value of y is 23°.

Measure of Angle A is 67°, as Angle A and B are vertical and equal in measure

Measure of Angle C is 113°, because the sum of angles on a line are equal to 180°, and are supplementary.

Measure of Angle D is also 113°, because it is vertical to Angle C.

Answer:

2ln5 + ln4 + ln5

Step-by-step explanation:

Think about how we can write 500 in terms of 4 and 5.

[tex]500 = 5^2*(4*5)[/tex]

So ln(500) can be written as ln(5^2*4*5)

Using log rules [tex]log_b(x*y)=log_b(x)+log_b(y)\\logb(x^a)=a*log(x)[/tex]

we can rewrite ln(500) to 2ln5 + ln4 + ln5

Answer:

7/5

Step-by-step explanation:

1/2 + 1/5

probability that at least one of the two students fail is 7/5