Use multiplication to solve the proportion
7/16 = x/4

Answer:

-7Q + 6 + 5Q = 15 - 7  Answer: q=−1

p+5+p=3(2+p) Answer: p=−1

(A + 4) + 6A = 2 (2 + 3A) Answer: a=0

Step-by-step explanation:

−7q+6+5q=15−7

Step 1: Simplify both sides of the equation.

−7q+6+5q=15−7

−7q+6+5q=15+−7

(−7q+5q)+(6)=(15+−7)(Combine Like Terms)

−2q+6=8

−2q+6=8

Step 2: Subtract 6 from both sides.

−2q+6−6=8−6

−2q=2

Step 3: Divide both sides by -2.

−2q/−2=2/−2

q=−1

p+5+p=3(2+p)

step 1: Simplify both sides of the equation.

p+5+p=3(2+p)

p+5+p=(3)(2)+(3)(p)(Distribute)

p+5+p=6+3p

(p+p)+(5)=3p+6(Combine Like Terms)

2p+5=3p+6

2p+5=3p+6

Step 2: Subtract 3p from both sides.

2p+5−3p=3p+6−3p

−p+5=6

Step 3: Subtract 5 from both sides.

−p+5−5=6−5

−p=1

Step 4: Divide both sides by -1.

−p/−1=1/−1

p=−1

a+4+6a=2(2+3a)

Step 1: Simplify both sides of the equation.

a+4+6a=2(2+3a)

a+4+6a=(2)(2)+(2)(3a)(Distribute)

a+4+6a=4+6a

(a+6a)+(4)=6a+4(Combine Like Terms)

7a+4=6a+4

7a+4=6a+4

Step 2: Subtract 6a from both sides.

7a+4−6a=6a+4−6a

a+4=4

Step 3: Subtract 4 from both sides.

a+4−4=4−4

a=0

Answer:   [tex]\dfrac{49}{99}[/tex]

Step-by-step explanation:

There are 61 boys --> 38 girls

A) 19 chose football: 5 are girls --> 14 are boys

B) 38 girls: 28 chose running, 5 chose football --> 5 girls chose tennis

C) 31 students chose tennis: 5 are girls --> 26 are boys.

D) 61 boys: 14 chose football, 26 chose tennis --> 21 boys chose running.

[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&14&5&19\\Tennis&26&5&31\\\underline{Running}&\underline{\quad 21\quad}&\underline{\quad 28\quad}&\underline{\quad 29\quad}\\Total&61&38&99\end{array}}[/tex]

Total running = 21 boys + 28 girls = 49

Total students = 99

[tex]\dfrac{\text{Total running}}{\text{Total students}}=\large\boxed{\dfrac{49}{99}}[/tex]

Answer:

Step-by-step explanation:

The minute hand of a clock overtakes the hour hand at intervalsof M minutes of correct time. The clock gains or loses in a day by=(720/11−M)(60×24/M) minutes.

Here M = 64. The clock gains or losses in a day by

=(720/11−M)(60×24/M)=(720/11−64)(60×24/64)

=16/11(60×3/8)=2/11(60×3)=360/11=32(8/11) minutes.

Answer:B

Step-by-step explanation: x is less than 1 so it is a open circle on the graph and x is greater than or equal to -1 so it is a closed circle on -1, B has both of these so B is the answer

Answer:

These are two equilateral triangles and all the sides of an equilateral triangle are equal. The question even says so so that's the answer, all the sides of the equilateral triangles are equal so all the sides equate to each other

Answer:

The slope of new figure A'B'C' = -1.2

A'B' = 3p units

A'C' = 3q units

Step-by-step explanation:

The value of each of the corresponding length of dilated figures (new image) = scale factor multiplied by the corresponding length in original figure.

scale factor = 3

Length of AB = p units

the length of AC = qunits

the length of BC = runits

A'B' = 3p units

A'C' = 3q units

B'C' = 3r units

slope of new figure = slope of previous figure

The slope remains the same = -1.2

The slope of the new figure is mathematically given as

dS=1.2

Question Parameter(s):

The slope of AB is -1.2.

The length of AB is punits

The length of AC is qunits

The length of BC is runits.

Generally, the lengths of the new region are mathematically given as

A'B' = 3p units

A'C' = 3q units

B'C' = 3r units

In conclusion, with the new region consistent in its increase across all regions the slope will remain

dS=1.2

Read more about Arithmetic

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Answer:

Step-by-step explanation:

The vertex of a parabola is directly in between the focus and the directrix. That means that the vertex of this parabola is at (1/2, 5). A parabola wraps itself around the focus and away from the directrix, so this parabola opens to the left. One other thing that we need to know is the distance between the vertex and the focus, the p value in the equation. So here's the equation we need (it's not a y= equation, though):

[tex]-(y-k)^2=4p(x-h)[/tex]

So here's what we know from the info above:

p = 5/2

h = 1/2

k = 5

and filling in:

[tex]-(y-5)^2=4(\frac{5}{2})(x-\frac{1}{2})[/tex] and simplifying:

[tex]-(y-5)^2=10(x-\frac{1}{2})[/tex] and then solving for x:

[tex]-\frac{1}{10}(y-5)^2+\frac{1}{2}=x[/tex]

Answer:

Its the last option. On the bottom.

Step-by-step explanation:

You need to Solve for x to find the zeroes of the equation.

x-1=0 So one x is at 1.

x+4=0 So the other x is at -4.

This graph is also not negative so it does not get flipped across the x-axis

The graph of the function [tex]f(x) = (x - 1)(x + 4)[/tex] is graph (d)

The equation of the function is given as:

[tex]f(x) = (x - 1)(x + 4)[/tex]

From the above function, we have the zeros of the function to be:

1 and -4

This means that:

Hence, the graph is graph (d)

Read more about quadratic functions at:

https://brainly.com/question/1214333

Answer:

B

Step-by-step explanation:

it is not a function because it fails the vertical line test,

A vertical line intersect the graph no more than once.

Step-by-step explanation:

Our polynomial is x²+30x +c with a missing value c

c should make this polynomial expression a perfect square

x²+ 30x+c

x² + 2*15*x +c

x²+2*15*x+15² ⇒ c = 15²=225

(x+15)²

Answer:

Step-by-step explanation:

each term has h^1

each term's coefficient is divisible by 12

12h( 3, h^5, 4h^4)

In a 30-60-90 triangle with short leg length x and hypotenuse length 8. the value of x in the triangle is 8 [tex]\sqrt{3}[/tex] / 3.

A right-angle triangle is a triangle that has a side opposite to the right angle the longest side and is referred to as the hypotenuse.

In a 30-60-90 triangle the ratio of the side lengths is 1 : 2 : [tex]\sqrt{3}[/tex]

To find the length of the short leg, x, you can create this proportion:

x / 8 = 1 / [tex]\sqrt{3}[/tex]

x = 8 × 1 / [tex]\sqrt{3}[/tex]

x = 8 / [tex]\sqrt{3}[/tex]

By rationalizing the denominator by multiplying the numerator and denominator by  [tex]\sqrt{3}[/tex].

x = 8 [tex]\sqrt{3}[/tex] / 3

Learn more about the right triangle;

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Answer:

Step-by-step explanation:

if the number of votes is 25, 12 is not majority

but if the number is 23 then 12 is majority

Answer:

30 books

Step-by-step explanation:

1. Find what 2/3 of Brett's books is.

2/3 of 72 or 0.667 x 72 = 48

2. Find what 2/3 of Charlie's books is.

2/3 of 27 or 0.667 x 27 = 18

3. Find the difference between 2/3 of Brett's books (48) and 2/3 of Charlie's books (18).

48 - 18 = 30

Adam has 30 books.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer: $10.50

Step-by-step explanation:

Given the following :

Number of people entering the park = X

Mean number of people = 3

Fixed admission fee = $6

Additional fee per passenger = $1.50

Therefore, mean total paid by a car entering the park :

MEAN Total = Admission fee + (additional fee * mean number of people entering the park)

mean Total = $6 + ($1.50 * 3)

Mean total = $6 + $4.50 = $10.50

Answer:

b) P(more than 10) = 2/9

c) P(less than 7) = 2/9

Step-by-step explanation:

a) Yaniq spins both spinners and then adds up the results together.

The results are as follow:

5

7

9

6

8

10

7

9

10

These are a total of 9 outcomes.

b) What is the probability that Yaniq gets a total of more than 9?

The probability is given by

P = Number of favorable outcomes/Total number of outcomes

For this case, the favorable outcomes are all those outcomes where the total score is more than 9.

Count the number of times Yaniq got a score of more than 9.

Yes right!

2 times (10 and 10)

P(more than 10) = 2/9

c) What is the probability that Yaniq gets a total of less than 7?

For this case, the favorable outcomes are all those outcomes where the total score is less than 7.

Count the number of times Yaniq got a score of less than 7.

Yes right!

2 times (5 and 6)

P(less than 7) = 2/9

Answer:  C) A = 6, B = -15

Step-by-step explanation:

In order to have infinitely many solutions, you must end up with 0 = 0 when adding the equations together.

 4x  -  Ay  =  15

-4x  + 6y  =  B  

    (6 - A)y = 15 + B

       ↓               ↓

  6 - A = 0      15 + B = 0

        6 = A             B = -15

Answer:

C

Step-by-step explanation:

TOOK THE TEST

Complete question:

The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?

Answer:

Juice A = 15

Juice B = 35

Step-by-step explanation:

Given the following:

Juice A:

Let juice A = a

35% pure fruit juice

Juice B:

Let juice B = b

85% pure fruit juice

We need to make 50 pints of juice from both: that is ;

a + b = 50 -------(1)

In terms of pure fruit:

a = 0.35 ; b = 0.85 ;

Our mixed fruit juice from a and b should be 70% pure fruit = 0.7

Mathematically,

0.35a + 0.85b = 50(0.7)

0.35a + 0.85b = 35 -------(2)

Multiply (2) by 100

35a + 85b = 3500 --------(3)

We can then solve the simultaneous equation:

a + b = 50 -------(1)

35a + 85b = 3500 --------(3)

Multiply (1) by 35

35a + 35b = 1750 -----(4)

35a + 85b = 3500 ---(5)

Subtract (5) from (4)

-50b = -1750

b = 35

Substitute b = 35 into (2)

0.35a + 0.85(35) = 35

0.35a + 29.75 = 35

0.35a = 35 -29.75

0.35a = 5.25

a = 5.25/0.35

a = 15

Juice A = 15

Juice B = 35

Answer:

Step-by-step explanation:

[tex]\left(4x-6\right)+\left(3x+6\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=4x-6+3x+6\\Group\:like\:terms\\=4x+3x-6+6\\\mathrm{Add\:similar\:elements:}\:4x+3x=7x\\=7x-6+6\\-6+6=0\\\\=7x[/tex]

Answer:

7x

Step-by-step explanation:

i took the test

Answer:

Hope this is correct and helpful

HAVE A GOOD DAY!

Step-by-step explanation:

If a perfect die is cast, the probability of obtaining a 5 is 1/6.

Answer:

the sum of p amd 7

hopefully this helped :3

Answer:

D

Step-by-step explanation:

Since addings answer is a sum

p+7

D

Answer:

Number of pendant made = 10

Step-by-step explanation:

Given:

Sides of triangle = 2 in , 2 in , 1.5 in

Total wire = 5 ft = 5 × 12 = 60 in

Find:

Number of pendant made.

Computation:

Perimeter of 1 pendant = 2 in + 2 in + 1.5 in

Perimeter of 1 pendant = 5.5 in

Number of pendant made = Total wire / Perimeter of 1 pendant

Number of pendant made = 60 / 5.5

Number of pendant made = 10.90

Number of pendant made = 10 and 1 pendant incomplete

Answer:

B

Step-by-step explanation:

Here, we want to know the kind of relationship a correlation value of 0.45 represents

Generally the perfect correlation value is 1, while a correlation score of zero shows no relationship between the two quantities.

Firstly, the value we have is positive, so we have a positive correlation, since it is closer to zero than 1, we can interpret the value as being a weak positive correlation

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) WXYZ is a rectangle              1. Given

2) ∠Z ≅ ∠Y                                 2. Definition of rectangle

3)  WZ ≅ XY                              3.  Definition of rectangle

4) ZY ≅ ZY                                 4. Reflexive property

5) ΔWZY ≅ ΔXYZ                      5. SAS

6) WY ≅ XZ               6. CPCT -Corresponding parts of congruent triangles

The diagonals of rectangle are congruent

Answer:

1: d. 3054^3

2: d. 20x

Step-by-step explanation:

1)

Well to find the volume of a sphere we use the following formula,

[tex]\frac{4}{3}\pi r^3[/tex]

So the radius is 9.

9*9*9 = 729

729*pi = 2290.22104447

So it is 2290 rounded to the nearest whole number.

2290 * 4/3 = 3053.3333333

Thus,

the answer is d. [tex]3054^3[/tex]

____________________________________________________________

So we have to factor 25x^2 - 9,

which is [tex]\left(5x+3\right)\left(5x-3\right)[/tex].

So if the l and w are 5x + 3 and 5x - 3,

= 10x

10x + 10x = 20x,

Thus,

the answer is d. 20x

Answer:

40 or 16+6+6+6+6

Step-by-step explanation:

To find the surface area of a 3d figure, we can imagine all of its faces laid down on a flat plane. In this case, we would have a square, and four congruent triangles. Now all we have to do is find the areas of each shape and add them up.

4 is the base of the pyramid, so it's also the square's side length. Since a square has four equal sides, our square's length and width are both 4.

4*4 = 16

For every triangle we have, the base is 4 and the height is 3. The area of a triangle can be found using the formula A=(bh)/2. We plug in the values:

A = (4*3)/2

A = (12)/2

A = 6

Since we have 4 triangles, the surface area is:

16+6+6+6+6 = 40

Answer:

16+6+6+6+6

Step-by-step explanation:

KHan

Answer:

Step-by-step explanation:

Given the total God diva chocolate contained in a box to be equal to 52 identical chocolates.

If 31 have caramel filling, the amount of walnut filling will be 52-31 = 21. This means 21 remaining chocolate will contain walnuts.

Probability = expected number of outcomes/total outcome

If we are to find the probability that the chocolate chosen at random contains walnuts, then our expected outcome will be 21 and the total outcome will be total God diva chocolate contained in the box  which is 52.

The probability that the chocolate chosen at random contains walnuts = 21/52