Write the equation of the line that has a slope of 4 / 3 and passes through the point ( 0, - 3 ).

Answer:

8

Step-by-step explanation:

square the whole equation to get

[tex] {m}^{2} + \frac{1}{ {m}^{2} } = 9[/tex]

then minus one from both sides of the equation to get 8

Answer: To construct a 99% confidence interval for the mean number of books people read, we can use the following formula:

CI = X ± Z*(S/sqrt(n))

where:

X = sample mean (11.3)

S = sample standard deviation (16.6)

n = sample size (1005)

Z = the z-score for the confidence level (99%)

To find the z-score for the 99% confidence level, we can look up the value in a standard normal distribution table or use a calculator. The z-score for a 99% confidence level is 2.576.

Substituting the values into the formula, we get:

CI = 11.3 ± 2.576*(16.6/sqrt(1005))

CI = 11.3 ± 2.576*(0.524)

CI = 11.3 ± 1.35

Therefore, the 99% confidence interval for the mean number of books people read is (9.95, 12.65). We can be 99% confident that the true population mean falls within this interval.

Step-by-step explanation:

Answer:

8 seconds

Step-by-step explanation:

-2t^2+9t+56=0

-2t^2+16t-7t+56=0

-2t(t-8)-7(t-8)=0

(-2t-7)(t-8)=0

-2t-7=0 or t-8=0

t-8=0

t=8

The side length of the unknown segment x in the triangle has a value of 40.1cm

To find the unknown side x, we use the sine rule

The Law of Sines (or Sine Rule) is very useful for solving triangles:

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

It works for any triangle and it says 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

To find the third angle in the triangle, we use the known rule of the sum of angles in a triangle which is equal to 180°

unknown angle = 180° - 90°- 55° = 35°

Using the sine rule let us find the side x

23/sin35 = x/sin90

23/0.5736 = x/1

from here we cross multiply to get

0.5736x = 23

We can find the value of x by dividing both sides by 0.5736

x = 23/0.5736

x = 40.1cm

Hence, the value is 40.1 cm

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The probabilities of picking the real numbers are 0.52 and 0.88, respectively

The probabilities in this case, is the area covered by each region

Using the above as a guide, we have the following:

Real number between 3 and 5

Here, we have the area to be

Region B

The area of region B is 0.56

So, we have

Probability = 0.56

Real number between 3 and 7

Here, we have the area to be

Region B and Region C

The areas of these regions are 0.56 and 0.32

So, we have

Probability = 0.56 + 0.32

Probability = 0.88

Hence, the probability is 0.88

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Answer:64

Step-by-step explanation:

27.5------100%

17.6--------x

x=64

Answer:y=6-X

Step-by-step explanation:

To leave y on it’s on on the right hand side we need to subtract X
X+y-X= y

What you do on the left hand side, you do the same on the right hand side

6-X

final equation would be:

X+y-X=6-X

Simplifying we get :

y=6-X (FINAL ANSWER)

Answer:

[tex]2\frac{7}{24}[/tex]

Step by step explanation:

just do the math it aint hard tbh

Answer:

[tex]2\frac{7}{24}[/tex]

Step-by-step explanation:

To work this out, we first need to change the fractions into mixed numbers...

Now we have to flip the second fraction around so our question will turn into a multiplication...

Now solve...

Hope this helps, have a lovely day! :)

The total feet of steel wire needed to secure the pole is 26 using Pythagoras Theorem.

What is Pythagorean Theorem?

A fundamental idea in mathematics pertains to the lengths of the sides of a right triangle and is known as the Pythagorean theorem. It claims that the hypotenuse's square length, which is the side that faces the right angle, equals the sum of the squares of the lengths of the other two sides of any right triangle. The Pythagorean theorem, which is named after the ancient Greek mathematician Pythagoras who originally proved the theorem, has extensive applications in areas including geometry, trigonometry, and physics.

Let the length of the wire = x.

Using Pythagoras Theorem we have:

x² = 12² + 5²

x² = 144 + 25

x² = 169

x = √(169)

x = 13

For two steel wires:

2(13) = 26 ft.

Hence, the total feet of steel wire needed to secure the pole is 26.

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Answer:

1a) Increment in price = 5500 - 4500 = 1000 Naira

1b) Percentage increase in price = (increment in price / old price) x 100%

= (1000 / 4500) x 100%

= 22.22%

2) Marked price = selling price / (1 - discount percentage)

= 3000 / (1 - 0.1)

= 3333.33 Naira

3) Total cost of 30 crates of eggs = 30 x 30 = 900 Naira

Commission = (4/100) x 900

= 36 Naira

4) Commission = (7/100) x 49000

= 3430 Naira

5) Discount = marked price - selling price

= 44.48 - 39.28

= 5.20 Naira

6) Discount = (245 - 225) / 245 x 100%

= 8.16%

7) Commission = (3/100) x 33

= 0.99 Naira

8) New salary = old salary + 5% of old salary

= 250 + (5/100) x 250

= 262.50 Naira

9) Marketed price = selling price / (1 - discount percentage)

= 55 / (1 - 0.05)

= 57.89 Naira

10) Marketed price = selling price + discount

= 845 + 55

= 900 Naira

Percentage discount = (discount / marked price) x 100%

= (55 / 900) x 100%

= 6.11%

Step-by-step explanation:

You do not have enough baking powder.

A mixed number is a value that is made up of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is 1 1/2.

In order to determine if you have enough baking powder, multiply 2 1/4 by 9. The teaspoons of baking powder that is needed for 4 1/4 servings = teaspoons needed for one serving x number of serving

2 1/4 x 4 1/4

= 9/4 x 17/4 = 153 / 16 = 9 9/16

9 9/16 is greater than 9 so you do not have enough baking powder.

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The area of the triangle in the diagram is 87.55 squared centimeters.

A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.

The area of a triangle is expressed as;

Area A= 1/2 × b × h

Where b is the base and h is the height of the trinagle.

From the image;

Plug the given values into the above formula and solve for the area of the triangle.

Area = 1/2 × base × height

Area = 1/2 × 17cm × 10.3cm

Area = 87.55 cm²

Therefore, the area is 87.55 squared centimeters.

Option D) 87.55 cm² is the correct answer.

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From the quadratic equation, we found the new dimensions:

Length =  14.85 feet

Width = 18.85 feet.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type

f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of

f (x).

The current dimensions of the farm are 10 feet by 14 feet.

Length l = 10 feet

Width w = 14 feet

Area a = l * w = 10 * 14 = 140 sq. feet.

Now the new area is doubled.

A = 2a = 2 * 140 = 280 sq.feet

The new dimensions are:

L = l + x = 10 + x

W = w + x = 14 +x

A = (10+x)(14+x)

280 = 140 + 10x + 14x + x²

x² + 24x - 140 = 0

This is a quadratic equation.

Solving the equation, we get

x = 4.85, -28.85

Neglecting the negative value, we get the value of x as 4.85.

Therefore from the quadratic equation, we found the new dimensions:

L = 10 + 4.85 = 14.85 feet

W = 14 + x = 14 + 4.85 = 18.85 feet.

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Therefore , the solution of the given problem of expressions comes out to be  the expression's precise number is 8/15.

There is a need for calculations like variable multiplication, dividing, joining, and currently removing. If you combined them, you'd get the following: A mathematical formula, some data, and an equation. Values, elements, mathematical operations like equation additions, deductions, errors, and subdivisions, as well as mathematical formulas, make up a statement of truth. It is possible to assess and analyse words and sentences.

Here,

A right triangle with an opposite side of 8 and a hypotenuse of 17 can be completed by adding the missing side using the Pythagorean equation. Make x the neighbouring side. Then:

=> x² + 8² = 17²

=> x² = 17² - 8²

=> x² = 225

=> x = 15

The triangle therefore has edges of 8, 15, and 17. As a result, the neighbouring angle's tangent is 15/8 and the sine of the angle across from the side of length 8 is 8/17. (since tangent is opposite over adjacent). In order to determine the cotangent, we can take the inverse of this tangent:

Coefficient

=> [sin⁻¹ 8/17] = 8/15

As a result, the expression's precise number is 8/15.

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Answer:

Step-by-step explanation:

1. 1 - 408

2. 15/136

3. 1/2

4. 24%

The area of the triangles are 81.77 square units, 333.50 square units, 207 square units and 52.21 square units

Given the triangles as the parameters, the area can be calculated as

Area = 1/2absin(C)

Using the above formula as a guide, we have the following equations

Triangle 7 = 1/2 * 15 * 13 * sin(57 degrees)

Triangle 7 = 81.77 square units

Triangle 8 = 1/2 * 28 * 24 * sin(83 degrees)

Triangle 8 = 333.50 square units

Triangle 9 = 1/2 * 23 * 18 * sin(90 degrees)

Triangle 9 = 207 square units

Triangle 10 = 1/2 * 15 * 7 * sin(96 degrees)

Triangle 10 = 52.21 square units

Hence, the area of triangle 10 is 52.21 square units

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Answer:

B) [tex]\frac{3}{2}[/tex] % of 400

Step-by-step explanation:

A) 2% of 150 = 3

Start by expressing the percent as a decimal by dividing the percent by 100

2% -> 0.02

Next multiply the percent by the number given

0.02 * 150 = 3

B)  [tex]\frac{3}{2}[/tex] % of 400 = 6

Start by expressing the percent as a decimal by dividing the percent by 100

3/2% -> 0.015

Next multiply the percent by the number given

0.015 * 400 = 6

C) 5% of 60

Start by expressing the percent as a decimal by dividing the percent by 100

5% -> 0.05

Next multiply the percent by the number given

0.05 * 60 = 3

D) 6% of 50

Start by expressing the percent as a decimal by dividing the percent by 100

6% -> 0.06

Next multiply the percent by the number given

0.06 * 50 = 3

After calculating all of the questions, we can see that the common product is 3, making B) the one that is not equal to the rest.

The given sequence is a geometric sequence, where the common ratio (r) between any two consecutive terms is:

r = 3/1.5 = 2

We need to find the sum of the first 10 terms of this sequence. Let's denote the first term (a₁) as 1.5 and the tenth term (a₁₀) as a.

The formula to find the sum of the first n terms of a geometric sequence is:

Sₙ = a(1 - rⁿ)/(1 - r)

Substituting the values, we get:

a = 1.5 x 2^9 = 768

S₁₀ = 1.5(1 - 2¹⁰)/(1 - 2) = 1.5(1 - 1024)/(-1) = 1.5 x 1023

Therefore, the sum of the first 10 terms of the given sequence is 1.5 x 1023, which is approximately equal to 1.53 x 10³=1534,5

We use the additiοn prοperty οf equality tο simplify this tο FA = RN, which is what we wanted tο prοve.

The substitutiοn prοperty οf equality states that if twο expressiοns are equal, then οne can be substituted fοr the οther in any equatiοn οr expressiοn withοut changing the truth οf that equatiοn οr expressiοn.

Step:

The prοοf starts with the given that FRAN. We want tο prοve that FARN is true. We start by using the segment additiοn pοstulate tο add RA tο bοth sides οf FR tο get FR + RA = FR + RA.

We then use the additiοn prοperty οf equality tο simplify this tο FR + RA = FR + RA. Next, we use the segment additiοn pοstulate again tο add AN tο bοth sides οf FR + RA tο get FR + RA + AN = FR + RA + AN.

We then use the substitutiοn prοperty οf equality tο replace AN with FR, which gives us FR + RA + FR = FR + RA + FR.

We simplify this tο FR + RA = FR + RA + FR and then use the segment additiοn pοstulate again tο add FA tο bοth sides οf RA tο get RA + FA = RA + FA.

Finally, we use the additiοn prοperty οf equality tο simplify this tο FA = RN, which is what we wanted tο prοve.

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Answer:

θ = arctan(10/62) ≈ 8.8°

Step-by-step explanation:

Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:

tan(θ) = 10/x

We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.

Answer: a) To find the number of working days on which under 18,000 bottles are filled, we need to calculate the z-score for this value:

z = (18,000 - 20,000) / 2000 = -1

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587. Therefore, the approximate number of working days on which under 18,000 bottles are filled is:

0.1587 x 260 ≈ 41

b) To find the number of working days on which over 16,000 bottles are filled, we need to calculate the z-score for this value:

z = (16,000 - 20,000) / 2000 = -2

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -2 standard deviations is approximately 0.0228. Therefore, the approximate number of working days on which over 16,000 bottles are filled is:

0.0228 x 260 ≈ 6

c) To find the number of working days on which between 18,000 and 24,000 bottles are filled, we need to calculate the z-scores for these values:

z1 = (18,000 - 20,000) / 2000 = -1

z2 = (24,000 - 20,000) / 2000 = 2

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587, and the probability of a value being less than 2 standard deviations is approximately 0.9772. Therefore, the approximate number of working days on which between 18,000 and 24,000 bottles are filled is:

(0.9772 - 0.1587) x 260 ≈ 236

Step-by-step explanation:

Answer:

the answer is (-infinity,1/3)Union (1/3,infinity)

Hence, 7200 units were produced throughout the period equivalently as WIP multiplied by the percentage of completion.

The percentage sign (%) is used to indicate it. When a student receives a score of 80% on a test, for instance, it signifies that 80 of the 100 questions were properly answered by the student. Alternatively, the result can also be expressed as a fraction of 80/100, or as 0.8 in decimal form. In order to express a portion or component of a whole, percentages are utilized. It is a practical technique to contrast values of various magnitudes on an equivalent scale.

given

The steps to determine the equivalent production are as follows:

Total units input: 8000

A typical loss is 400 units, or 5% of 8000 units.

Consider there to be no anomalous loss because none has been reported.

Counted in total units: 8000 - 400 = 7600 units

Units completed: 7600 less 1000 (closing WIP) equals 6600 units.

Equivalent production equals completed units plus closing WIP multiplied by the percentage of completion, which equals 6600 + 1000 x 60%, or 6600 + 600, or 7200 units.

Hence, 7200 units were produced throughout the period equivalently as WIP multiplied by the percentage of completion.

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Function is increasing in the domain of interval (1, ∞).

A quadratic function is a mathematical function of the form:

f(x) = ax² + bx + c

where "a", "b", and "c" are constants, and "x" is the variable.

From the given table of ordered pairs, we can see that the function k is a continuous quadratic function that passes through the points (-1, 0), (0, 2), (2, 5), (3, 4), and (4, 5).

We can estimate the slope of the function between each pair of consecutive points in the table. For example, between (-1, 0) and (0, 2), the slope is positive, so the function is increasing in the interval (-1, 0). Between (0, 2) and (2, 5), the slope is also positive, so the function is increasing in the interval (0, 2). However, between (2, 5) and (3, 4), the slope is negative, so the function is decreasing in the interval (2, 3).

Finally, between (3, 4) and (4, 5), the slope is positive, so the function is increasing in the interval (3, 4). Therefore, the function k is increasing over the intervals (-1, 0) and (3, 4).

So, the correct answer is option A: (1, ∞).

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Answer:

We know that the formula for the circumference (C) of a circle is:

C = 2πr

where r is the radius of the circle.

We are given that the circumference is 8πm, so we can write:

8πm = 2πr

Simplifying this equation by dividing both sides by 2π, we get:

r = 4m

Now that we know the radius of the circle, we can use the formula for the area (A) of a circle:

A = πr^2

Substituting the value we found for r, we get:

A = π(4m)^2

Simplifying this equation, we get:

A = π(16m^2)

A = 16πm^2

Therefore, the area of the circle is 16πm^2. The answer is C

the rate of change of the angle of elevation teta is  ∅ = tan⁻¹ 2.1275

Angle of Elevation is an equation used in math to describe the angle formed between the horizontal line and the line of sight when an observer looks upwards. It is always at a height that is greater than the height of the observer

Using ∅ = tan⁻¹ (x/2000)

Then we are to find the angle teta

Where x = 4255 ( substitution)

∅ = tan⁻¹ (4255/2000)

∅ = tan⁻¹ 2.1275

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Answer:

Step-by-step explanation:

Use the figure to complete the transformations.

1. Reflect the triangle across the y-axis.

2. Reflect the image across the x-axis.

The final image is the same as what single transformation?

a translation 2 units to the left and 2 units down

a reflection across the y-axis

a 180° rotation about the origin

a clockwise rotation 90° about the origin