The sum of 3x2 + x+8 and x? - 9 can be expressedas1) 4x2+x-12) 4x²+x-173) 4x+x-14) 3x + x - 1

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Answer:

Good thanks for points hehe

The algebraic expression for the area is:

A = (2H - 8)*H/2

Here we want to write the expression:

"the area of a triangle that has a base 8 inches less than 2 times wider than the height."

Remember that for a triangle of base B and height H, the area is:

A = B*H/2

So if the base is 8 inches less than 2 times the height, we can write:

B = 2*H - 8

Replacing that in the area equation we get:

A = (2H - 8)*H/2

That is the equation for the area.

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Answer:

31742

Step-by-step explanation:

\(26900 \times \frac{100 + 18}{100 } = 31742 \)

Answer:

17

Step-by-step explanation: First multiply 2.70 by 5 which would equal 13.50. Then, add 13.50 and 3.50 would equal 17.

Please give brainliest if this helps. Thanks!

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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There is sufficient statistical evidence at 5% level of significance that there is   relationship between degree attainment and AGEKDBRN for women.

What is ANOVA model for men?

To ascertain whether there are any statistically significant differences between the means of three or more independent (unrelated) groups, the one-way analysis of variance (ANOVA) is used.

An n-way ANOVA allows a researcher to employ more than two independent variables (with n being the number of independent variables you have). For instance, any disparities in IQ scores can be investigated concurrently by country, gender, age group, ethnicity, etc.

Relationship between degree attainment and AGEKDBRN for women

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The best representation of the number of tiles that will be needed to cover the Floor is 80 tiles.

The number of tiles needed to cover the floor, we can calculate the total area of the floor and divide it by the area of each tile.

The area of the floor is given by the product of its length and width: 15 feet * 12 feet = 180 square feet.

The area of each tile is given by the product of its length and width: 1.5 feet * 1.5 feet = 2.25 square feet.

To find the number of tiles needed, we divide the total area of the floor by the area of each tile:

Number of tiles = (Total area of the floor) / (Area of each tile) = 180 square feet / 2.25 square feet = 80 tiles.

therefore, the best representation of the number of tiles that will be needed to cover the floor is 80 tiles.

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The maximum volume of the cylinder is approximately 1257 cubic centimeters.

The volume V of a right circular cylinder with radius r and height h is given by:

V = πr²h

Substituting the given expressions for the radius and height of the cylinder, we get:

V = πx²(800/πx - x)

Simplifying the expression, we get:

V = 800x - πx³

To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

dV/dx = 800 - 3πx² = 0

3πx² = 800

x² = 800/3π

x ≈ 6.43

Substituting this value of x back into the expression for V, we get:

V ≈ 1257

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Answer:

-7/3

Step-by-step explanation:

You take two ( X,Y) points and subtract them to find the slope of the line.

23-16/-6-(-3) = -7/3

Answer: 112 degrees

Step-by-step explanation:

The angles have the same measure because of the corresponding angles theorem.

\(\huge\boxed{112^\circ}\)

To solve this problem, we need to understand the basic rules of transversals across parallel lines.

When a line crosses another line or lines, it is a transversal.

When the two lines it crosses are parallel, the eight angles formed have interesting properties that we can use.

For this question, we will look at corresponding angles. If two angles meet these two conditions, they are congruent:

These two conditions are met for \(\angle JIK\) and \(\angle GFI\), so they are congruent and their measures are equal.

This means that \(m\angle JIK=m\angle GFI=\boxed{112^\circ}\)

Answer:

Step-by-step explanation:

!od

7x=96

Answer:

range is the y part and domain is the x so the range is the y coordinates

-6,-3,-2,-2,1,4

Step-by-step explanation:

The value of 14.5% of 1,800 is 261 by using the concept of percentage.

In mathematics, a percentage is a value or ratio expressed as a fraction of 100.

The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.

A % is a relative figure that indicates one-tenth of a quantity. One percent (symbolized 1%) is the one-hundredth part; consequently, 100 percent denotes the complete amount, and 200 percent specifies twice the supplied amount.

Given,

14.5% of 1,800

=(14.5/100)×1800

=261

Therefore, the answer is 261.

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The skirt = s

The sweater is twice as much so 2s

The total sum has to equal or be less than $75

Inequality = s + 2s <=75

Simplify to 3s <= 75

Most the skirt can cost: solve for s:

3s <= 75

Divide both sides by 3

S <= 25

The most the skirt can cost is $25

Answer:

Inequality: s ≤ 25

Max skirt cost: $25

Step-by-step explanation:

s = skirt cost

x =  sweater cost

Since the sweater costs twice as much as the skirt, an equation will look like this:  

x = 2s

Since her budget is $75, that means she can spend $75 or less but not more, so another equation will look like this:

x + s ≤ 75

Plug 2s into the bottom equation

2s + s ≤ 75

Add up the terms

3s ≤ 75

Divide both sides by 3, the coefficient, to isolate s, the variable.

3s/3 ≤ 75/3

s ≤ 25

That means she can spend $25 or less on a skirt.

Henry's rate of movement in the two legs can be determined by applying the formula of speed. Thus, his speed during his first leg is 0.6 hours.

The speed of an object is a measure of how fast it moves in a given time. So that;

Speed = \(\frac{Distance}{Time}\)

In the given question, let the rate of his fist leg be represented by x. Thus;

⇒ Time = \(\frac{Distance}{Speed}\)

For the first leg of his trip;

Time taken, \(T_{1}\)  = \(\frac{32}{x}\)

For the second leg of his trip;

Time taken, \(T_{2}\) = \(\frac{12*2}{x}\)

                   = \(\frac{24}{x}\)

Given that the total trip takes 1 hour, then:

\(T_{1}\) + \(T_{2}\) = 1 hour

\(\frac{32}{x}\)  + \(\frac{24}{x}\) = 1

\(\frac{56}{x}\) = 1

x = 56

Then;

\(T_{1}\) = \(\frac{32}{x}\) = \(\frac{32}{56}\)

    = \(\frac{4}{7}\)

\(T_{1}\) = \(\frac{4}{7}\) hours

\(T_{2}\) = \(\frac{24}{x}\) = \(\frac{24}{56}\)

   = \(\frac{3}{7}\)

\(T_{2}\) = \(\frac{3}{7}\) hours

Henry's speed during the first leg of his trip is \(\frac{4}{7}\) hours (0.6 hours).

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Answer:

the answer is c

Step-by-step explanation:

Its c because U have 3.99 for your first movie rent and all you need to do is multiply it times how much movie rents there are.

So, thats why its c.

Answer:

c

Step-by-step explanation:

i took the test

To solve this problem we need to calculate the volumes of each of the pyramids individually.

The formula for the volume V of a pyramid is

Where

A_B: base area

h: height

For the first pyramid

For the second pyramid

The difference in volumes

The difference between the volumes of the pyramids is 214167 square meters.

Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

The equation of the trigonometric graph, which is the graph of a sinusoidal function is; y = 4·sin(2·(x - π) + 1

A sinusoidal function is a function that repeats with time, such that it is a periodic function. The form of a sinusoidal function is a sine or a cosine function, which can be expressed as; f(x) = A·sin(ω·x + φ).

The description of the graph of the trigonometric function can be presented as follows;

The coordinate of the maximum point is; (π/4, 5)

The coordinate of the next minimum point is; (3·π/4, -2.5)

The coordinate of the y-intercept is; (0, 1)

A general form of the equation of a sinusoidal function is; y = A·sin(B·(x - C)) + D

Where;

A = The amplitude, which is the average value of the function

B = The frequency which is the number of cycles per interval

C = The phase shift, which is the horizontal shift of the function.

D = The vertical shift of the function

The amplitude A is therefore; A = (5 - (-3))/2 = 4

The period = 2·π/B = 2 × (3·π/4 - π/4) = π

Therefore;

π = 2·π/B

B = (2·π)/π = 2

The vertical shift = (The maximum y-value + minimum y-value)/2

Therefore; The vertical shift is; (5 + (-3))/2 = 1

The y-intercept indicates that we get;

1 = 4·sin((2·(0 - C)) + 1

(1 - 1)/4 = 0 = sin(2·(0 - C))

0 = sin(2·(0 - C))

arcsine(0) = 2·C

arcsine(0) = 2·π

Therefore; arcsine(0) = 2·π = 2·C

C = 2·π/2 = π

Therefore; y = 4·sin(2·(x - π)) + 1

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Answer(s):

\(\displaystyle y = 4cos\:(2x - \frac{\pi}{2}) + 1 \\ y = -4sin\:(2x \pm \pi) + 1 \\ y = 4sin\:2x + 1\)

Step-by-step explanation:

\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

OR

\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = 4cos\:2x + 1,\) in which you need to replase “sine” with “cosine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{4}\:unit\) to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD \(\displaystyle \frac{\pi}{4}\:unit,\) which means the C-term will be positive; so, by perfourming your calculations, you will arrive at \(\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.\) So, the cosine equation of the sine graph, accourding to the horisontal shift, is \(\displaystyle y = 4cos\:(2x - \frac{\pi}{2}) + 1.\) Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits \(\displaystyle [\frac{3}{4}\pi, -3],\) from there to \(\displaystyle [-\frac{\pi}{4}, -3],\) they are obviously \(\displaystyle \pi\:units\)apart, telling you that the period of the graph is \(\displaystyle \pi.\) Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 1,\) in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

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52s is the maximum time that she can take on her last lap and still make the team.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).

The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

We need to find the maximum time (in seconds) that she can take on her last lap and still make the team

Let x be the maximum time (in seconds) that she can take on her last lap

60=(63+62+65+58+x)/5

300=63+62+65+58+x

300=248+x

Subtract 248 on both sides

300-248=x

x=52s

Hence, 52s is the maximum time that she can take on her last lap and still make the team.

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Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

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For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer: each base angle in an isosceles right triangle measures 45 degrees.

Step-by-step explanation:

In an isosceles right triangle, two sides have equal lengths, and one angle is a right angle (90 degrees).

Since it is an isosceles triangle, the two base angles (the angles opposite the equal sides) must be congruent, meaning they have the same measure.

To find the measure of each base angle, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let's denote the measure of each base angle as "x". Then, the sum of the three angles in the triangle can be expressed as:

x + x + 90 = 180

Simplifying the equation:

2x + 90 = 180

Subtracting 90 from both sides:

2x = 90

Dividing both sides by 2:

x = 45

Answer

400% Probability Of Sarah Getting Picked !

Step-by-step explanation:

So first 2000 x 19% = 380%