Write the expression as a single trigonometric function.
cos 5x cos 6x- sin 5x sin 6x

Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

[tex]y = \frac{5 \sqrt{3} }{2} [/tex]

y=4.33

Answer:

Step-by-step explanation:

cotθ = cosθ/sinθ = 2/3

sinθ = 3/√(2²+3²) = 3/√13

cscθ = 1/sinθ = √13/3

Answer:

251.5 cm

Step-by-step explanation:

1 m = 100 cm

1 cm = 10 mm

2 m + 50 cm + 15 mm =

= 2 m * (100 cm)/m + 50 cm + 15 mm * (1 cm)/(10 mm)

= 200 cm + 50 cm + 1.5 cm

= 251.5 cm

Answer:

It cannot be 0

Step-by-step explanation:

it can also be positive number :2/4

it can be odd number too:3/9

it is bigger than numerator bcoz we have to divide it for numerator

So, 0 number cannot be put as denominator in fraction is true statement

Answer:

8 minuets

Step-by-step explanation:

24min/3miles = 8

Answer:

8 minutes.

Step-by-step explanation:

If we divide 24 minutes by 3 miles, your answer will be 8 minutes.

Answer:

180000 people

1 : 2

$40

80 stores

Step-by-step explanation:

1.)

Population in 2020 are equal : Let population =

City A increased by 20% From 120,000 in 2015

(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000

Hence, city A = 144,000.

Since, city A and B have equal population ; city B also has a population of 144000 in 2020.

Let population in 2015 = x

(1 - 0.2) * x = 144000

0.8x = 144000

x = 144000/0.8

x = 180,000

2.)

Let proportion of 20% butter = x and proportion of 50% butter = 1 - x

0.2x + 0.5(1 - x) = 0.4

0.2x + 0.5 - 0.5x = 0.4

-0.3x + 0.5 = 0.4

-0.3x = 0.4 - 0.5

-0.3x = - 0.1

x = 0.1/0.3

x = 0.3333

(1-x) = 1 - 0.33333 = 0.6666%

0.3333% of 20% butter

0.6666% of 50% butter

Hence ;

0.3333 : 0.6666

1 : 2

3.)

Let original price of book = x

Discount on sale = 30%

Sale price = $28

Sale price = original price * (1 - discount)

$28 = (1 - 0.3) * x

$28 = 0.7x

x = $28/0.7

x = $40

4.)

Let total number of stores = x

Store surveys needed = 32

40% of total stores = 32 stores

0.4x = 32

x = 32 / 0.4

x = 80

Answer:

Step-by-step explanation:

the arrows from the picture tells us that TV is parallel to RS

since TS is a transversal that cuts the 2 parallel lines TV and RS than ∠S =x

(alternate interior angles)

sum of angles in a Δ is 180° so x+x+2x = 180°, 4x =180°, x= 45°

2x = 45*2 = 90°

Answer:

(-2,2) and (-3,-4)

Step-by-step explanation:

by graphing the line and parabola, you should get this graph

Answer:

12

Step-by-step explanation:

Scale factor of 4

CD = 3

3 · 4 = 12

Length of C'D' is 12 units

Answer:

12 units

Step-by-step explanation:

The original segment CD = 3 units

Scale factor is 4.

3 x 4 = 12

Answer:

Option C

Step-by-step explanation:

thankful that there are graphing tools. see screenshot

Answer: C

<BFE is 148 degrees

Step-by-step explanation:

We have angles <BFC (57 degrees) and <CFD (34 degrees), but what is <DFE?

1. The angle symbol in the vertexes shows that <BFC is congruent to <DFE, meaning that they are the same

2. Knowing this, we can safely say that <DFE is equal to 57 degrees because <BFC is also 57 degrees.

3. Now, we have all the angles we need to find out <BFE.

4. <BFC+<CFD+<DFE=<BFE

5. Substitute to get

57+34+57=<BFE

91+57=<BFE

148=<BFE

6. Now we know that the answer is 148 degrees.

Answer:

The slope is undefined.

Step-by-step explanation:

The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.

Answer:

20'×15 in 54 inches

Step-by-step explanation:

The Best as a pool should be rectangular in shape and 54inches deep for safety of life's

The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi r^{2}[/tex]h

The volume of the cylindrical pool that has a 3.3 m radius and is 1.8 m deep is;

=  [tex]\pi r^{2}[/tex]h

[tex]= 3.14 (3.3)^2 (1.8)\\\\= 61.55 m^3[/tex]

The volume of the rectangular pool that is 20' x 15' in 54 inches deep ;

V = 20 x 15 x 54

V = 16,200 cubic meter.

The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.

Learn more about volume;

https://brainly.com/question/1578538

#SPJ2

If y (0) = -1/3, then

-1/3 = 1 / (1 + C e ⁻⁰)

Solve for C :

-1/3 = 1 / (1 + C )

-3 = 1 + C

C = -4

So the particular solution to the DE that satisfies the given initial condition is

[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]

Answer:

The point is a solution

Step-by-step explanation:

y = x^2

Substitute the point into the equation and see if it is true

0 = 0^2

0=0

True

9514 1404 393

Answer:

  arithmetic; common difference of 5

Step-by-step explanation:

It usually works well to check differences first. Here, they are ...

  8 -3 = 5

  13 -8 = 5

These are the same value, so the sequence is arithmetic with a common difference of 5.

9514 1404 393

Answer:

  y = -9x +49

Step-by-step explanation:

The slope of line b is the same as the slope of line a. That can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -8)/(2 -1) = -9

The y-intercept can be found from the given point using the formula ...

  b = y - mx

  b = 13 -(-9)(4) = 13 +36 = 49

Then the slope-intercept equation of line b is ...

  y = -9x +49

9514 1404 393

Answer:

  (b)  0 = -78

Step-by-step explanation:

Subtracting 6 times the first equation from the second will give ...

  (4x +15y) -6(2/3x +5/2y) = (12) -6(15)

  0 = -78

Answer:

the answer is b

Step-by-step explanation:

9514 1404 393

Answer:

  6 units

Step-by-step explanation:

The dilation factor is 2, so the length of A'B' will be 2 times the length of AB.

AB can be seen to be 3 units, so A'B' will be 2×3 = 6 units.

Answer:

0.3736

Step-by-step explanation:

46.7 percent of  [tex]\frac{4}{5}[/tex] is 0.3736.

To find 46.7% of [tex]\frac{4}{5}[/tex].

So,

[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]

[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]

⇒ [tex]0.3736[/tex]

Therefore,  46.7% of  [tex]\frac{4}{5}[/tex] is 0.3736.

Know more about percentages here:

https://brainly.com/question/24304697

#SPJ2

Answer:

135

Step-by-step explanation:

Given that :

Total score obtained by Peter, Jan and Maxim = 269

Let :

Peter's score = x

Jan's score = y

Maxim's score = z

x + y + z = 269

x > (y + z)

For x to be greater Than y + z ;

Then x > (269 / 2) ; x > 134.5

The least possible x score is 135

Hence, Peter's least possible score is 135.

More information pleaseeeeeeee

15,068 mi/hr

Step-by-step explanation:

[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]

[tex]=15,068\:\text{mi/hr}[/tex]

The speed of 22100 feet per second will be 15068.18 miles per hour.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.

Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,

22100 ft /s = ( 22100 x 3600 ) / 5280

22100 ft/s = 79560000 / 5280

22100 ft/s = 15068.18 miles per hour

To know more about unit conversion follow

https://brainly.com/question/28901160

#SPJ2

Answer:

[tex]\angle P[/tex]

Step-by-step explanation:

Given

[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]

[tex]PQ = 20[/tex]     [tex]QR = 16[/tex]    [tex]PR = 12[/tex]

[tex]ST = 30[/tex]       [tex]TU = 34[/tex]    [tex]SU = 16[/tex]

See attachment

Required

Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]

Considering [tex]\triangle PQR[/tex]

We have:

[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse

So, we have:

[tex]\sin(P) = \frac{16}{20}[/tex]

Divide by 4

[tex]\sin(P) = \frac{4}{5}[/tex]

Hence:

[tex]\angle P[/tex] is correct

Answer:

A or <P

Step-by-step explanation:

on edge 2021

Answer:

a)

The null hypothesis is: [tex]H_0: p_M - p_W = 0[/tex]

The alternative hypothesis is: [tex]H_1: p_M - p_W > 0[/tex]

b) For men is of 0.49 and for women is of 0.36.

c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Men:

98 out of 200, so:

[tex]p_M = \frac{98}{200} = 0.49[/tex]

[tex]s_M = \sqrt{\frac{0.49*0.51}{200}} = 0.0353[/tex]

Women:

72 out of 200, so:

[tex]p_W = \frac{72}{200} = 0.36[/tex]

[tex]s_W = \sqrt{\frac{0.36*0.64}{200}} = 0.0339[/tex]

a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.

At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:

[tex]H_0: p_M - p_W = 0[/tex]

At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:

[tex]H_1: p_M - p_W > 0[/tex]

b. What is the sample proportion for men? For women?

For men is of 0.49 and for women is of 0.36.

c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?

From the sample, we have that:

[tex]X = p_M - p_W = 0.49 - 0.36 = 0.13[/tex]

[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0353^2 + 0.0339^2} = 0.0489[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error, so:

[tex]z = \frac{0.13 - 0}{0.0489}[/tex]

[tex]z = 2.66[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.

Looking at the z-table, z = 2.66 has a p-value of 0.9961.

1 - 0.9961 = 0.0039.

The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Answer:

[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]

Answer:

21

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = x / 7 sqrt(3)

7 sqrt(3)  tan 60 = x

7 sqrt(3) sqrt(3) = x

7*3 = x

21 = x