Express as a trinomial (3x+8) (x+10)

Answer:

15.7 in  

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826  

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]

It checks.

Answer:

y=135

x=45

Step-by-step explanation:

x= 45

It is an isosceles so

180-90=90

90/2= 45  

y=135

angles on a straight line add up to 180 so

180-45=135

Hope this helps!

Answer:

Solution : Option D

Step-by-step explanation:

The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )

x = 5cos(t) ⇒ x / 5 = cos(t)

y = 2sin(t) ⇒ y / 2 = sin(t)

Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )

( x / 5 )² = cos²(t)

+ ( y / 2 )² = sin²(t)

_____________

x² / 25 + y² / 4 = 1

Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.

[tex]\sf{\implies Range = Highest \: - lowest }[/tex]

→ Range of Lewistown = 74 - 64

→ Range of Lewistown = 10 .

→ Range of Hamersville = 71 - 55

→ Range of Hamersville = 16 .

☆ Range of Hamersville - Range of Lewistown

→ 16 - 10

→ 6

Answer → The range for Hamersville is 6 more than the range for Lewistown .

Answer:

Step-by-step explanation:

If  the path of the longest shot put by the Women’s track team at Sun Devil U is modeled by h(x) = -0.015x² + 1.08x + 5.8 where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground, to determine h(24), we will have to substitute x = 24 into the modeled equation as shown;

[tex]h(x) = -0.015x^2 + 1.08x + 5.8\\\\if \ x = 24;\\\\h(24) = -0.015(24)^2 + 1.08(24) + 5.8\\\\h(24) = -0.015(576)+25.92+5.8\\\\h(24) = -8.64+31.72\\\\h(24) = 23.08\\[/tex]

Hence the value of the height at the horizontal distance of 24 feet is 23.08 feet to 2 decimal place.

Answer:63

Step-by-step explanation:

Answer:

C. [tex] -\frac{5}{2}} [/tex]

Step-by-step explanation:

If two lines on a graph are perpendicular to each other, their slope is said to be negative reciprocals of each other. This means the slope of one, is the negative reciprocal of the other.

This can be represented as [tex] m_1 = \frac{-1}{m_2} [/tex]

Where, [tex] m_1, m_2 [/tex] are slopes of 2 lines (i.e. the red and green lines given in the question) that are perpendicular to one another.

Thus, the slope of the red line would be:

[tex] m_1 = \frac{-1}{\frac{2}{5}} [/tex]

[tex] m_1 = -1*\frac{5}{2}} [/tex]

[tex] m_1 = -\frac{5}{2}} [/tex]

The slope of the red line = [tex] -\frac{5}{2}} [/tex]

Answer:

x = 1/e^-5 - 1

Step-by-step explanation:

–2 ln (x + 1) − 3 = 7

–2 ln (x + 1) = 10

ln (x + 1) = –5

x + 1 = e^-5

x = e^-5 - 1

x = 1/e^-5 - 1

the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:

1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.

2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.

3. Simplify: -2 ln(x + 1) = 10.

4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.

5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.

6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.

7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.

8. Simplify: x ≈ -0.9933.

Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

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Answer:

[tex]\Huge \boxed{x=24}[/tex]

Step-by-step explanation:

[tex]-5x + 12x - 8x = -24[/tex]

Combine all like terms.

[tex](-5+ 12- 8)x = -24[/tex]

[tex]-x=-24[/tex]

Multiply both sides by -1.

[tex]x=24[/tex]

Answer:

x must be 24

Step-by-step explanation:

I assume you meant " -5x + 12x - 8x = -24

Combine the x terms on the left side, obtaining -x = -24.

Then x must be 24

Answer:

Rate= 3 1/3%

Or Rate= 3.33%

Step-by-step explanation:

Final amount collected= $700

Initial amount given out= $600

Interest made= Final amount - initial amount

Interest made= $700-$600

Interest made= $100

Type of interest rate = simple

Number of years = 5

PRT/100= interest

R=(100*interest)/(PT)

R= (100*100)/(600*5)

R= 10000/3000

R= 10/3

R= 3 1/3%

Or R= 3.33%

Answer:

54°

Step-by-step explanation:

Let ∠CYX=x

AB║CD

∠AXE=∠CYX  (corresponding angles)

∠AXE=3∠CYX-108

x=3x-108

3x-x=108

2x=108

x=108/2=54°

∠AXE=∠CYX=x=54°

∠BXY=∠AXE=54° (Vertically opposite angles)

Answer:  Statement 1: postulate; Statement 2: definition

Step-by-step explanation:

Here, Statement 1:If parallel lines have a transversal, then corresponding angles are congruent.

which is a fact, and hence it is postulate.

Statement 2: A line has an infinite number of points extending in opposite directions.

which is an explanatory statement of a 'line', hence it is 'definition.

So the correct option is Statement 1: postulate; Statement 2: definition

Answer:statement 1 and statement 2 postulate

Step-by-step explanation:

Answer:

Put 0 in the box.

Step-by-step explanation:

The value x = 0 if replaced in the given equation will always make the denominator zero.

Best Regards!

Answer:

the number that is halfway between 250 and 300 is 275

Step-by-step explanation:

250+300= 550/2= 275

The number i,e halfway is 275.

[tex]= (250 + 300) \div 2\\\\= 550 \div 2[/tex]

= 275

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Answer:

97290

Step-by-step explanation:

47 different people can win first

47

Now there are only 46 people left

46 different people can win second

46

45 different people can win third

47*46*45

97290

Answer: x=3.2     AC= 42.8

Step-by-step explanation:

As point B lies at segment AC      AC=AB+BC

Otherwise we can write the equation

5x+9x-2=11x+7.6

14x-2=11x+7.6

14x-2+2=11x+7.6+2

14x=11x+9.6

14x-11x=11x-11x+9.6

3x=9.6

x=9.6:3

x=3.2

AC= 11*x+7.6= 11*3.2+7.6=35.2+7.6=42.8

Answer:

Ashley= 15

Milan= 11

Carlos= 105

Step-by-step explanation:

Let, A, M and C denotes Ashley, Milan and Carlos respectively.

A+M+C= 131 (according to the question)

Here,

C= 7A

A= M+ 4

So, M= A - 4

Now,

A+M+C = 131

or, A+ A-4+ 7A = 131 (putting the values)

or, 9A - 4 = 131 (adding like terms i.e. A + A + 7A)

or, 9A = 131 + 4

or, 9A = 135

or, A = 135 / 9

So, A = 15

C= 7A = 7×15= 105

M= A-4 = 15 - 4 = 11

Answer:

see below

Step-by-step explanation:

√p = 9/16

We need to square each side, not take the square root

(√p)^2 =( 9/16)^2

p = 81/256

Answer:

a. True

b. true

c. false

d. false

e. false

Step-by-step explanation:

a. true

polutation = 25% = 0.25

sample = n= 12

n x p

= 12 x o. 25 = 3 and 3 is less than 10

12(1 - p)

= 12 x 0.75

= 9 and is less than 10

b. True

the sample distribution of the population is normal when

sample size x population > or equal to 10

40 x 0.75

= 30 and 30 is greater than 10

c. false

50 x 0.25 = 12.5

50 x 0.20 = 10

z = 10 - 12.5/sqrt(12.5)

= -2.5/3.54

= -0.70

H0: Young american family who delayed

H1: young american family who did not delay

p(z = -0.70)

0.2420>0.005

therefore we accept the null hypothesis

d. false

150 x 0.20 = 30

150 x 0.75 = 37.5

z = 30 - 37.5/sqrt(37.5) = -7.5/6.12 = -1.22

p(z = -1.22) = 0.1112 > 0.05

therefore we do not reject the null hypothesis

e. false

se1 = sqrt(p(1-p)/n

se2 = sqrt(p(1-p)/3n

se2 = 1/sqrt(3)se2

Answer:

see below

Step-by-step explanation:

First we need to find the slope

m = ( y2-y1)/ ( x2-x1)

   = (60-64)/( 10-0)

   = -6/10

   = -2/5

The y intercept is (0,64)

The slope intercept form of the equation is

y = mx+b  where m is the slope and b is the y intercept

y = -2/5 x + 64  where y is in the thousands of feet

m = -2/5 * 1000 = -400 ft / minute

The height decreases since the sign is negative

The height decreases 400 ft per minute

The y intercept is (0,64)

64 is in the thousands of ft

64*1000 = 64,000 ft

When it starts, it is at 64,000 ft

The descent starts at a cruising altitude of 64,000 ft

answer is 71.08745247

in mix form or in short form it is =

71/23/263

Answer:

16

Step-by-step explanation:

7x+20+2x-5=159

9x+15=159

9x=159-15

9x=144

x=16

[tex]|\Omega|=_{12}C_3=\dfrac{12!}{3!9!}=\dfrac{10\cdot11\cdot12}{2\cdot3}=220\\|A|=4\cdot3\cdot5=60\\\\P(A)=\dfrac{60}{220}=\dfrac{3}{11}\approx0,273[/tex]

Answer:

0.273

Step-by-step explanation:

Total number of balls is 4+3+5 = 12

There are 6 ways to draw 3 different colors (WBR, WRB, BWR, BRW, RWB, RBW) each with a chance of 4/12 · 3/11 · 5/10 = 1/22

So the total chance is 6 · 1/22 = 6/22 = 3/11 ≈ 0.273

Answer:

5 and 3/32 of an inch.

Answer:

0.14

Step-by-step explanation:

The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14

The area under the curve shaded is 1 to 2 is 0.14

Probabilities are used to determine the chances of an event

The shaded region represents the probability of the z-scores

The shaded region 1 to 2 is represented as:

P(1 < z < 2) =

Using the probability of z-score, we have the formula

P(1 < z < 2) = P(z < 2) - P(z < 1)

From the given standard normal table:

P(z < 2) = 0.9772

P(z < 1) = 0.8413

So, we have:

P(1 < z < 2) = 0.9772 - 0.8413

P(1 < z < 2) = 0.1359

Approximate

P(1 < z < 2) = 0.14

Hence, the area under the curve shaded is 1 to 2 is 0.14

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Answer:

Probability= 0.5

Step-by-step explanation:

A 14 sided die is rolled

Total number of occurrence= 14 numbers

Total odd numbers present

= 1,3,5,7,9,11,13

Total number of odd numvers present

= 7

Probability= number of required outcome/total possible outcome

Probability= 7/14

Probability= 0.5

Answer: No, the orders are not independent.

Step-by-step explanation:

If event 1 has some possible outcomes, suppose that we choose a given outcome 1 with a probability P1, and event 2, also with different possible outcomes, we can select an outcome 2, that has a probability P2, and the two events are independent (meaning that the outcome in event 1 does not affect the outcome in event 2, and vice versa)

Then the probability of outcome 1 and outcome 2 happening at the same time is equal to the product of their individual probabilities.

P = P1*P2.

In this case, event 1 is the selection of the pizza, and outcome 1 is the selection of the square pizza, with a probability of 55%.

Event 2 is the selection of the drink, outcome 2 is the order of a soft drink, with a probability of 72%.

If those two events were independent, then the probability that a customer orders a square pizza and a soft drink would be:

P = 0.55*0.72 = 0.396 (or 39.6%)

But we know that the actual probability is 48%.

So this is larger, which means that the outcomes are not independent.

Answer:

t = (448 hrs/ week) / (30 hrs / week)

Step-by-step explanation:

Number of times park opens in a week = 7

Number of ticket booth = 8

Opening hours = 10am - 6pm = 8 hours per day

Max working hours per ticket seller per week = 30 hours

Therefore each booth works for 8 hours per day,

Then ( 8 * 7) = 56 hours per week.

All 8 booths work for (56 * 8) = 448 hours per week

If Max working hours per ticket seller per week = 30 hours,

Then muninim number of workers required (t) :

Total working hours of all booth / maximum number of working hours per worker per week

t = (448 hrs/ week) / (30 hrs / week)

Answer:

21

Step-by-step explanation:

√1500 ≈ 38.7

round that up to 39 and square it:

39² = 1521

Answer:

2. 20 oranges

3. 18 yellow tulips

4. 23 students