What is the ratio between 1 1/4 hours and 25 minutes?

The length of the wire attached to the pole is 20.62 feet

The pole is perpendicular to the ground in the direction of the point where the wire is attached to the ground to form a right angle triangle.

A leg of the triangle is 20 feet(length of the pole from the surface of the ground to the top)

The other leg is5 feet(distance from the base of the pole to the point where the wire is attached to the ground)

The third side of the right angle triangle is the hypotenuse(length of the wire)

Applying Pythagoras theorem;

Hypotenuse² = Opposite² + Adjacent²

= 20 feet ² + 5 feet²

= 400 + 25

Hypotenuse² = 425

Find the square root of both sides

Hypotenuse = √425

= 20.6155

Approximately,

Hypotenuse = 20.62 feet

In conclusion, the hypotenuse side of the right angle triangle is 20.62 feet

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The number of cans of soup bought is 8 and the number of frozen dinners purchased is 3.

s + f = 11 equation 1

350s + 650f = 4750 equation 2

Where:

The elimination method would be used to solve for the required values:

Multiply equation 1 by 350

350s + 350f = 3850 equation 3

Subtract equation 2 from equation 3 :

300f = 900

f = 900 / 300

f = 3

Substitute for f in equation 1 :

s + 3 = 11

s = 11 - 3

s = 8

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Answer:

The answer is (-4x² + x + 2)

Step-by-step explanation:

(2x² - 4x + 3) + (5x - 6x² - 1)

open the brackets

2x² - 4x + 3 + 5x - 6x² - 1

rearrange the priority order

2x² - 6x² - 4x + 5x + 3 - 1

combine like terms

-4x² + x + 2

Thus, The answer is (-4x² + x + 2)

Answer:

[tex] \frac{7}{6} [/tex]

Answer:

y= [tex]\frac{4}{3}[/tex] x+ [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

         -3x-4y=12

1. First we need to get the equation in the form of y=mx+c to do this we add 3x to both sides and then divide it by -4 on each side to get

      (add 3x to both sides) = -4y=3x+12

      (divide each side by -4)= y= -[tex]\frac{3}{4}[/tex] x -3

2. to find the perpendicular gradient we find the reciprocal of the original gradient

            the reciprocal of -[tex]\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex]

3. we can check this by multiplying them and seeing of we get -1

           -[tex]\frac{3}{4}[/tex] x  [tex]\frac{4}{3}[/tex] = = -1

4. we then sub in the gradient  [tex]\frac{4}{3}[/tex] in y=mx+c this gives us

      y= [tex]\frac{4}{3}[/tex]x +c

5. to find the value of c we substitute the coordinates into the equation to get ( we do this by expanding the brackets and getting c on it own)

       -3=  [tex]\frac{4}{3}[/tex](-4) +c

       -3= -[tex]\frac{16}{3}[/tex] +c

        [tex]\frac{7}{3}[/tex]=c

6. we sub  [tex]\frac{7}{3}[/tex]=c  back into  y= [tex]\frac{4}{3}[/tex]x +c  this gives us

          y= [tex]\frac{4}{3}[/tex]x + [tex]\frac{7}{3}[/tex]

7. Therefore our final answer is

          y= [tex]\frac{4}{3}[/tex]x + [tex]\frac{7}{3}[/tex]

The answer is cos 60° × cos 30° + sin 60° × sin 30° = √3/2.

The fundamental guidelines and procedures to simplify any algebraic statement are as follows:By multiplying factors, remove any grouping symbols like brackets and parenthesis.

Simplify each term.

34+14

Combine fractions.

Combine the numerators over the common denominator.

3+14

Simplify the expression.

Add 3

and 1

44

Divide 4by 4

=  1.

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Answer:

d. [tex]5x^3[/tex] is a monomial

Step-by-step explanation:

⭐What is a monomial?

D is correct because the expression [tex]5x^3[/tex] consists of 1 term only.

⭐What is a linear polynomial?

⭐What is the degree of a polynomial?

A is incorrect because the largest exponent in the expression [tex]x^2 + 5x -3[/tex] is 2, which makes expression A a quadratic polynomial.

⭐What is a binomial?

B is incorrect because the expression [tex]x^2 + 4x - 1[/tex] consists of 3 terms, not 2 terms. B is a trinomial.

C is incorrect because the expression [tex]x+1[/tex] consists of 2 terms, not 1 term. C is a binomial.

⭐if this response helped you, please mark it the "brainliest"!⭐

Do not reject H(0). There is not sufficient evidence to a manufacturer of transistors claims that its transistors will last an average of different than 1000 hours. at 0.01 significance level.

In the given question, a manufacturer of transistors claims that its transistors will last an average of 1000 hours.

To maintain this average, 25 resistors are tested each month.

We may assume that the distribution of the lifetime of a transistor is normal.

We have to calculate a sample that has a mean of 1010 and a standard deviation of 60.

So let us consider

X : Life time of a transistor

So we have

N=25

x=1010

s=60

Since sample size n(25≤30) is small and population standard is unknown so we use t statistic for hypothesis testing.

Now our null and alternate hypotheses are given as:

H(0): μ=1000

H(1): μ≠1000 (two tailed test)

Under Null hypothesis our test statistic is;

t=(x-μ)/(s/√n)

t=(1010-1000)/(60/√25)

t=0.83

Critical Value:

t(α,(n-1))=t(0.01, 24)

t(α,(n-1))=2.80

We have given level of significance α=0.01 and also we find the t-score 0.83 and degree of freedom=24

p value

The Excel formula is used to calculate the p value is:

P value =2×(1- (t(24) > 0.83))

P value =2×(1-0.7926)

P value =2×0.2074

P value =0.4147

Since p value=0.42 greater than α=0.01 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected and we claims that its transistors will last an average of 1000 hours.

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The person is 8.325 miles far from her home and she should walk in the direction of 64.86° North Of East to head directly home .

In the question ,

from the figure ,

we see that point O is  home of the person ,

it is given that person leaves the home and walks 4 miles west to point A , then 5 miles in south west direction to the point B .

So ,distance OA = 4 miles

AB = 5 miles .

In triangle OAB ,

angle OAB = 45+90 = 135°

Using Cosine Rule ,

OB² = OA² + AB² - 2*OA*AB*Cos(135)°

= 16 + 25 + 28.2843 = 69.2843

So ,OB = √69.2843  = 8.325 miles .

Now using Sine Rule ,

Sinθ/OA = Sin(135°)/OB

Sinθ = 4*Sin(135°)/8.324

Sinθ = 0.339792

So , θ = 19.86°

hence the direction from North of East is

= 45° + θ

= 45° + 19.86°

= 64.86° North Of East .

Therefore , the distance is 8.325 miles and the direction is 64.86° North Of East .

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The p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year is 0.0060 and the value of test statistic is - 2.51

54% of business owners gave a holiday gift to their employees. a survey of business owners conducted this year indicates that 32 of them plan to provide a holiday gift to their employees.

The survey results are based on a sample of 80 business owners

We need to find the value of test statistic.

Expected number = np  = 32

80 x p = 32

p = 0.4

This is a left tailed test

test statistic is (p^ - p)/√(pq/n)

= (0.40 - 0.54)/√(.54 - (1 - 0.54) / 80)

= 0.14/√((0.54 - 0.46)/80)

= -2.51

p value = P(z < - 2.51)

= 0.00060366

= 0. 0060

Therefore, the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year is 0.0060 and the value of test statistic is - 2.51

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The monthly income of the government service holder is Rs. 12000

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that: Rs. 85000 was exempted in the yearly income of a government service holder. If he paid tax Rs. 8850 in a year at the rate of 15%.

Let P represent the yearly income. We can write that:

15% (P - 85000) = 8850

0.15(P - 85000) = 8850

0.15P - 12750 = 8850

0.15P = 8850 + 12750

0.15P = 21600

P = 21600/0.15

P = 144000

So the yearly income is  Rs. 144000

Thus, the monthly income will be:

Rs. 144000 / 12 = Rs. 12000

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The rate at which Submarine B descends is 29.8 feet per hour.

The rate refers to the average speed of an object in motion from one point to another.

The rate can be determined by dividing the distance by the time.

The rate or average speed is the quotient between distance and time.

The distance descended by Submarine A = 193.5 feet (126 + 4 ½ x 15)

The time Submarine B descends = 6.5 hours

Submarine B's rate of descent = 29.77 feet (193.5/6.5) per hour

= 29.8 feet

Thus, we can conclude that Submarine B descends at the rate of 29.8 feet every hour, whereas, Submarine A descends 15 feet per hour.

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Answer:

Any line that is in the form

y =

Step-by-step explanation:

See the graph below.  Perpendicular means that the lines meet at 90°.  You will see the black line graphed that is x = 2.  Then you will see two graphs in red.  y = 6 and y = -1.  any line in the form y = some number will be perpendicular to x = 2.

(a) The hypothesis to analyze is H₀ : [tex]\mu_{f} = \mu_{m}[/tex]   v/s     H₁ :  [tex]\mu_{f} \neq \mu_{m}[/tex]

(b) the value of test stat is 1.585 and the p-value is 0.114  .

In the question ,

it is given that ,

the number of females is (n₁) = 504 and

mean (μ₁) = 3.13

the number of males is (n₂) = 400 and

mean (μ₂) = 2.87 .

Part(a) ,

the hypothesis to analyze whether the population means differ for females and males is ,

H₀ : [tex]\mu_{f} = \mu_{m}[/tex]   v/s     H₁ :  [tex]\mu_{f} \neq \mu_{m}[/tex]

Part(b)

given that df = 503 and standard error (SE) = 0.164 and α = 0.05 .

So , the test statistic  is :

t = (μ₁ - μ₂)/SE

= (3.13 - 2.87)/0.164

= 1.585

the p-value of the test can be calculated by :

P-Value = P(reject H)

= P(|t| > test stat)

= P(t > 1.585)

From the t table ,

we get the value as

= 0.114

the conclusion is p-value = 0.114 > 0.05 = alpha then we fail to reject the H₀  .

Therefore  , the (a) hypothesis is H₀ : [tex]\mu_{f} = \mu_{m}[/tex]   v/s     H₁ :  [tex]\mu_{f} \neq \mu_{m}[/tex] and

(b) the t stat is 1.585 and p value is 0.114 .

The given question is incomplete , the complete question is

For the 2015 general social survey, a comparison of females and males on the number of hours a day that the subject watched tv gave the following results.

Females = 504; mean 3.13

Males = 400; mean 2.87

(a) Set up the hypothesis of a significance test to analyze whether the population means differ for females and males .

(b) Conduct all parts of the significance test if df = 503 and standard error = 0.164 interpret the P-value and report the conclusion for a = 0.05 .

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The statement "considered multiple regression which is a sample at 36 observations for a given eggs and fitted why the 95% approximate prediction interval for individual why is wider than the corresponding approximate 95% confidence interval for the conditional mean" is false.

Here we have given the statement and we need to identify whether this one is true or not.

As we all know that then Confidence interval is narrower than the prediction interval because Prediction intervals must account for both the uncertainty in estimating the population mean, plus the random variation of the individual values.

Therefore the prediction interval is always wider than a confidence interval.

And also here the prediction interval will not converge to a single value as the sample size increases.

Therefore, the statement is incorrect.

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The answers to both subparts are shown:

(A) The expression is: 4x = 714

(B) Money she put in her savings account each week: $178.5

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Let's assume she works 7 days a week.

Then 7.5 * 16 = $120 (1-day earning)

30 days: 120 * 30 = 840

$18 each day on lunch: 18 * 7 = $126

Remaining: 840 - 126 = $714

A quarter of $714: 714/4 = $178.5

(A) The expression will be:

4x = 714

(B) Money she put in her savings account each week:

4x = 714

x = 714/x

x = $178.5

Therefore, the answers to both subparts are shown:

(A) The expression is: 4x = 714

(B) Money she put in her savings account each week: $178.5

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the correct answer is A cause × +5 is linear polynomial

The points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin are

(2–√,−2–√,2−22–√)

(−2–√,2–√,2+22–√)

Using Lagrange multipliers we attempt to find the extrema of f(x,y,z)=x2+y2+z2 given that g(x,y,z)=x−y+z−2=0 and that h(x,y,z)=x2+y2−4=0.

Given,

∇f=⟨2x,2y,2z⟩

∇g=⟨1,−1,1⟩

∇h=⟨2x,2y,0⟩

Extrema satisfy the condition that ∇f=μ∇g+λ∇h for some λ,μ∈R.

This is to say,

2x=2λx+μ

2y=2λy−μ

2z=μ

If λ=1 then μ=0 and so z=0, the g constraint tells us that x=y+2, and the h constraint tells us that y2+(y+2)2=4, meaning that either y=0 or y=2. This provides us with two crucial points in addition to the g constraint:

(2,0,0)

(0,−2,0)

Now assume λ≠1, and so

x=μ2−2λ

y=−μ2−2λ=−x

Since x=−y, we have that x=±2–√, y=∓2–√. Using the g constraint, our two critical points are

(2–√,−2–√,2−22–√)

(−2–√,2–√,2+22–√)

And then it's east to determine which is the max and which is the min out of these four critical points.

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Max Says that the product 30 x 10 by 4 has exactly four zeros is not true.

Multiplication is a method of finding the product of two or more numbers

We need to check whether product 30 x 10 by 4 has exactly four zeros

firstly we have to multiply thirty with ten

Now multiply 30×10=300

Which has two zeros and now we have to divide it by 4

300/4

Three hundred by four

75

Seventy five.

Hence, Max Says that the product 30 x 10 by 4 has exactly four zeros is not true.

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Answer:

One can of tomatoes needs 4 teaspoons of oregano.

Step-by-step explanation:

[tex]\frac{11}{44}[/tex] = [tex]\frac{1}{x}[/tex]  Cross multiply and solve for x

11x = 44  Divide both sides by 11

x = 4

One can of tomatoes needs 4 teaspoons of oregano.

The total number of fishes present in the lake on my 1 is 840.

The given data for the question-

September is equivalent to a percentage of tagged fish in May.

3/42 = 60/x

x = 60 *42 / 3

x = 840

Thus, the total number of fishes present in the lake on my 1 is 840.

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The answer of the given scientific multiplication is,  8.84 x 10^-1.

What is scientific multiplication?

Multiply the decimal numbers to multiply the numbers in scientific notation. Add the 10 power exponents after that. In scientific notation, place the new power of 10 with the decimal.

Given:

(6.8 x 10^2) x (1.3 x 10^-3)

We have to solve this using scientific multiplication.

First to multiply the decimals,

6.8 x 1.3 = 8.84

Now to solve

10^2 x 10^-3 = 10^(2-3) = 10^-1

⇒  (6.8 x 10^2) x (1.3 x 10^-3) = 8.84 x 10^-1

Hence, the answer of the given scientific multiplication is,  8.84 x 10^-1.

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Answer:

D

Step-by-step explanation:

The line of best fit is a line that represents the “average” between all of the points. It’s typically in the middle of all of the points. In this case, I’d go with D because 4 points lie on the line of best fit and the line trends sharply upwards, following the general direction of the points.

The answer is 18x10^4 using simple arithmetic calculations and exponential function.

What are arithmetic calculations?
Arithmetic calculations are mathematical operations that involve the addition, subtraction, multiplication, and division of real numbers. Arithmetic is used to solve problems and execute tasks in everyday life, and is an integral part of mathematics. It is also used to analyze data and solve equations. Arithmetic involves the use of numbers, symbols, and operations in order to solve problems. Examples of arithmetic operations include addition, subtraction, multiplication, division, and exponentiation. The order of operations is an important part of arithmetic, as it dictates which operations take precedence over others. Arithmetic is used in a variety of applications, such as in engineering, finance, education, and science. It can also be used to solve puzzles and games. Arithmetic calculations can be used to help people better understand the world around them, as well as to help them make better decisions in life.

Two exponential function having same base , then powers can be added or subtracted.

In given equation, base is of 10 and powers are 8 and -4.

now the power will be 4

and 3 and 6 get multiplied i.e. 18.

So, the answer is 18x10^4.

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The length of the sides of the special triangles, found using the relationship between the sides of the triangles are as follows;

(1) Length of the legs is 20 each

Length of the hypotenuse = 20·√2

(2) Length of the leg = 5

Length of the hypotenuse = 5·√2

5-50 a. Length of the leg is 10·√3

Length of the hypotenuse is 20

b. Length of the leg = 4

Length of the hypotenuse = 4·√2

c. Length of each leg = 8

d. Length of the leg = 9·√3

Length of the hypotenuse = 18

e. Length of the shorter leg = 4.5

Length of the longer leg = 4.5·√3

f. Length of the legs = 3·√2 each

5-51

What are triangles?

A triangle is a three sided polygon, that has a sum of interior angles of 180°

The lengths of the missing sides in the triangles found using the 30°–60°–90°, and 45°–45°–90°, triangle patterns are as follows;

In a 30°, 60°, 90° triangle, if the length of the shortest leg is x, the length of the hypotenuse is 2·x, and the length of the other leg is x·√3

In a 45°, 45°, 90° triangle, the length of the legs are the same, and the length of the hypotenuse is √2 multiplied by the length of one leg.

(1) The length of the legs are the same and equivalent to 20

The length of the hypotenuse side is 20·√2

(2) The length of the legs are the same and equivalent to 5

The length of the hypotenuse 5·√2

5-50 a. In the 30°, 60°, 90° triangle, the length of the adjacent, longer leg is 10·√3

The length of the hypotenuse side is 2·x

b. The triangle is a 45°, 45°, 90°, triangle

The length of the legs are 4 unit each

The length of the hypotenuse is 4·√2

c. The length of the hypotenuse in the 45°, 45°, 90° is 8·√2, therefore, the length of the legs are;

8 units each

d. The length of the shortest leg in the 30°, 60°, 90°, right triangle is 9, therefore, the length of the hypotenuse side is 2 × 9 = 18

The length of the longest leg is 9·√3

e. The length of the hypotenuse in the 30°, 60°, 90°, right triangle is 9 units, therefore, the length of the shortest leg is 4.5 units

The length of the longest leg is 4.5·√3

f. The length of the hypotenuse side of the 45°, 45°, 90°, right triangle is 6, therefore;

The length of the legs are 6/√2 = 3·√2

5-51

The dimensions of the side length of the special right triangles are;

In a 30°-60°-90° triangle, if the length of the shortest leg is x, then;

The length of the hypotenuse is 2·x

The length of the longer leg is x·√3

In a 45°-45°-90° right triangle, the length of the legs are the same, and the length of the hypotenuse is √2 multiplied by the length of one leg.

Please attached diagrams of the 45°, 45°, 90°, and the 30°, 60°, 90° triangles created with MS Word

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Answer:

none of the listed options

Step-by-step explanation:

the equation for x axis is y=0

Answer:

84

Step-by-Step Explanation: