3. Find the measure of x.
a 18°
b. 54°
C 126
d. 45

Answer:

-4 sqrt(7)/7

Step-by-step explanation:

csc theta = -4/3

csc theta = hypotenuse / opposite side

hypotenuse = 4  

opposite  = 3

Using the pythagorean theorem

a^2 + b^2 = c^2

3^2 + b^2 = 4^2

9+b^2 = 16

b^2 = 16-9

b^2 = 7

Taking the square root

sqrt(b^2) = sqrt(7)

b = sqrt(7)

We are in the third quadrant so only tan  and cot are positive

that means the x and y values are "negative"  so a = -3 and b = - sqrt(7)

sec theta = hypotenuse / adjacent

                = 4/ - sqrt(7)

rationalizing  

                   -4 sqrt(7)/ sqrt(7)* sqrt(7)

                = -4 sqrt(7)/7

Answer:

352 cm/s

Step-by-step explanation:

circ = 44pi

speed = distance * time

distance = circ * 4 = 176pi

speed = 176pi/0.5

Answer:

≈ 1106 cm/s

Step-by-step explanation:

linear speed = angular speed x radius of the rotation

v = ωr

v = linear speed (m/s)

ω = angular speed (radians/s)

r = radius of the rotation (m)

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

Given:

Linear speed is:

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

4.32÷18=0.24

Step-by-step explanation:

I used a calculator

Using "b", the expression for the sum of the number of baseballs Kris Byrant hit in two days is (135 + b).

As per data provided in the question statement, Kris Byrant hit "b" number of baseballs yesterday and he hit 135 baseballs today.

We have to find out the expression to express the sum of the number of baseballs Kris Byrant hit in two days using the variable "b".

As the question statement itself directs very clearly that We have to find out the expression to denote the sum of the number of baseballs Kris Byrant hit in two days using the variable "b", we will simply add the individual numbers of baseballs he hit on each day, i.e.,

(b + 135).

And then, we can use this expression to calculate the real number of baseball Kris Byrant hit in two days for (b = 120, say), i.e.,

If Kris Byrant hit 120 baseballs yesterday and he hit 135 baseballs today, he will have hit a total of (120 + 135) = 255 baseballs in two days.

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The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Answer:

C

Step-by-step explanation:

The area of the rectangle can be doubled by adding 2m to both length and width of the rectangle

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

The area of rectangle is given by the formula;

A = L × W

The current length is 10m and width is 3m, the area of this figure is

A = 10 * 3

A = 30m²

The area is double and this will becomes 2 * 30m² = 60m²

The length and width of the rectangle is;

60 = (x + 10) × (x + 3)

x = 2

He must add 2m to both length and width

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Answer:

40

Step-by-step explanation:

angle 1 and 4 are vertical angles therefore they have the same measure of 40 degrees

The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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Answer:

7.50

Step-by-step explanation:

i'm dumb

Answer:

He can buy 5 cartons of eggs

Step-by-step explanation:

Take $9.50 and subtract $2

Then divide that answer by $1.50

The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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The solution of the given expression will be 9/16.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²

= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²

= 9/16

Hence, The solution of the given expression will be 9/16.

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6/7 of people are not having a disease, the whole is 1 so the difference is:

2/3 of those having a disease is:

15 people are the 1/7 fraction of total people referred to quarantine.

The total number is:

3/5 of 105 people are male, that is:

Number of female is:

Answer:

\(\sf (i) \quad \dfrac{1}{7}\)

\(\sf (ii) \quad \dfrac{2}{21}\)

\(\sf (iii) \quad 315\:people\)

\(\sf (iv) \quad 126\: females\)

Step-by-step explanation:

If 6/7 of people who are quarantined do not have the disease then the fraction of people that do have the disease is:

\(\begin{aligned} \implies 1-\dfrac{6}{7} & =\dfrac{7}{7}-\dfrac{6}{7}\\\\ & =\dfrac{7-6}{7}\\\\ & =\dfrac{1}{7}\end{aligned}\)

Therefore, 1/7 of people in quarantine have the disease.

We are told that 2/3 of the people who have the disease come from abroad.  Therefore, the fraction of diseased people coming from abroad is 2/3rds of the diseased people:

\(\begin{aligned} \implies \dfrac{2}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{2}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{2 \times 1}{3 \times 7}\\\\ & = \dfrac{2}{21}\end{aligned}\)

Therefore, the fraction of diseased people who have come from abroad is 2/21.

We are told that 15 people who have the disease do not come from abroad.  So if 2/3 of the people who have the disease come from abroad, then 1/3 of the people who have the disease do not come from abroad.  Remember that 1/7 of the total people have the disease.

\(\begin{aligned} \implies \dfrac{1}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{1}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{1 \times 1}{3 \times 7}\\\\ & = \dfrac{1}{21}\end{aligned}\)

Therefore, 1/21 of the total number of people have the disease and do not come from abroad.

Therefore, 15 people are equal to 1/21 of the total number of people:  

\(\implies \sf Total\:number\:of\:people=15 \times 21 = 315\)

Therefore, the total number of people in quarantine is 315.

If 3/5 of the total are male, then 2/5 must be female.

\(\begin{aligned} \implies \dfrac{2}{5} \textsf{ of }315 & = \dfrac{2}{5} \times 315\\\\ & = \dfrac{2 \times 315}{5}\\\\ & = \dfrac{630}{5}\\\\& = 126 \end{aligned}\)

Therefore, 126 females are in quarantine.

Answer:

15 cups of orange juice

Step-by-step explanation:

Let u be 1 unit.

5u = 25 cups

u = 25÷5

= 5

3u = 5×3

= 15

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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Answer:

f÷g=2x+5x+2=7x+2

x=3

7×3+2=21+2=23

The value of  (f + g)(x) when x = 3, if f(x) = 2x and g(x) = 5x + 2, is 23.

The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).

Given:

f(x) = 2x and g(x) = 5x + 2

Calculate  (f + g)(x)  as shown below,

f(x) + g(x) = 2x + 5x +2

f(x) + g(x) = 7x + 2

Put x = 3

f(3) + g(3) = 7 × 3 + 2

f(3) + g(3) = 23

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Answer:

Set up an equation using these key terms:

Form the equation by piecing these key terms together:

63/100(63%) ×(of) X(The number being sought) = 792("-is 792)

63/100 × X = 792

(63/100 can be simplified to 0.63)

So, rewrite the equation to:

0.63 × X = 792

Solve for x!

0.63x = 792

Isolate 'x' by dividing 0.63 from both sides because the inverse operation of multiplication is division.

÷0.63 ÷0.63

x = 1,257.14285714 which can be rounded to 1,257.14.

Therefore, the number being sought is 1,257.14.

If you are dealt one card from a​ 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.

Since there are 4 aces in a deck of card 52 first step is to find the number of cards  not aces in a deck of 52

Number of cards  not aces in a deck = 52 -4

Number of cards  not aces in a deck = 48

Now let find the probability that you won't draw an ace.

Probability = 48/52

Probability = 24/26

Probability = 12/13

Therefore we can conclude that the probability is 12/13.

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Answer:

x^2+y^2=25

Step-by-step explanation:

bc x-0=x and ect.

The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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Answer:

y = (1/60) x² - (7/20) x + 49/30

Step-by-step explanation:

equation formula:    y = ax² + bx + c

pass (-1,2) (2,1) (7,0)

(-1,2):  a - b + c = 2   ... (1)

(2,1):   4a + 2b + c = 1   ... (2)

(7,0):   49a + 7b + c = 0   ... (3)

(2)-(1):  3a + 3b = -1   ... (4)

(3)-(2):  45a + 5b = -1   ... (5)

(4)*15-(5): 40b = -14         b = - 7/20   ... (6)

(4): 3a = -1 - 3*(-7/20) = 1/20        a = 1/60    ...(7)

(1): c = 2 - 1/60 + (-7/20) = 49/30        c =  49/30

equation:  y = (1/60) x² - (7/20) x + 49/30

Answer:

1.5r + 7 ≤ 30

Step-by-step explanation:

r = rides rode (that's sounds weird but funny lol)

Admission costs $7. Each ride costs $1.50, so the money he spends has to be less than or equal to $30

Mean:-

\(\\ \sf\longmapsto \dfrac{Sum\:of\:terms}{No\:of\;terms}\)

\(\\ \sf\longmapsto \dfrac{5+13+7+14+16+5+5}{7}\)

\(\\ \sf\longmapsto \dfrac{65}{7}\)

\(\\ \sf\longmapsto 9.2\)

Median:-

Answer:

\(\angle\,DGF=30^o\)

which agrees with the first answer listed among the possible options.

Step-by-step explanation:

Notice that if a circle is perfectly inscribed inside the triangle, the triangle must have the symmetries that correspond to an equilateral triangle (all equal sides). Such type of triangles have the three angles equal as well, and since they need to add to \(180^o\), they must measured each \(60^o\)

Now, the segment that joins the center of this symmetric triangle (also the center of the circle) with the triangle's vertices, has to bisect each each internal angle in equal parts.

Therefore, angle \(\angle\,DGF\) must measure half of  \(60^o\), that is:  \(30^o\)

Answer:

These are easy you should know

Step-by-step explanation:

But it looks like you got the answers already God Bless

Answer:

B and E

Step-by-step explanation:

the graph (Justine) shows the line

y = 2x

the line for Velma is

y = 4x

now we need to remember that the slope (inclination) of a line is the factor of x (so, 2 and 4 in the two line equations).

a slope is expressed as y/x and indicates how many units y changes when x changes a certain amount of units (like 1).

as described (and also confirmed by the graph) the x units are minutes, and the y units are meters.

so, as per her slope, Velma moves 4 meters in 1 minute.

and Justine moves 2 meters in 1 meter.

so, Justine is half as fast as Velma.

and therefore, Justine moves a shorter distance than Velma each minute.

Answer:

Step-by-step explanation:

B and E

A three-person jury can be selected from a pool of eleven people in 165 ways.

For the given question;

The total number of person in the pool = 11.

The number of jury selected = 3.

Thus, the combination will be ⁿCₓ.

Where, n = 11 and x = 3.

¹¹C₃ = 11!/3!(11 - 3)!

Simplifying;

¹¹C₃ = 165

Thus, the number of ways in which three jury can be selected from 11 pool of members is 165.

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Answer:

k = \(\frac{3}{4}\)

Step-by-step explanation:

given variation equation

y = kx

to find k substitute y = 3 and x = 4 into the equation and solve for k

3 = 4k ( isolate k by dividing both sides by 4 )

\(\frac{3}{4}\) = k