Need help plotting this on number line

Answer:

About 1.85 seconds and 13.15 seconds.

Step-by-step explanation:

The height (in feet) of the rocket t seconds after launch is given by the equation:

[tex]h = -16t^2 + 240 t[/tex]

And we want to determine how many seconds after launch will be rocket be 390 feet above the ground.

Thus, let h = 390 and solve for t:

[tex]390 = -16t^2 +240t[/tex]

Isolate:

[tex]-16t^2 + 240 t - 390 = 0[/tex]

Simplify:

[tex]8t^2 - 120t + 195 = 0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]

In this case, a = 8, b = -120, and c = 195. Hence:

[tex]\displaystyle t = \frac{-(-120)\pm \sqrt{(-120)^2 - 4(8)(195)}}{2(8)}[/tex]

Evaluate:

[tex]\displaystyle t = \frac{120\pm\sqrt{8160}}{16}[/tex]

Simplify:

[tex]\displaystyle t = \frac{120\pm4\sqrt{510}}{16} = \frac{30\pm\sqrt{510}}{4}[/tex]

Thus, our two solutions are:

[tex]\displaystyle t = \frac{30+ \sqrt{510}}{4} \approx 13.15 \text{ or } t = \frac{30-\sqrt{510}}{4} \approx 1.85[/tex]

Hence, the rocket will be 390 feet above the ground after about 1.85 seconds and again after about 13.15 seconds.

Answer:

A

Step-by-step explanation:

the factored form of the binomial expansion x^3 + 9x^2 + 27x + 27 is (x+3)^3

36×7

=252

Explaination :

First Multiply 6 and 7 we get 42 !

Write 2 and 4 will be added to the product of 3×7

We get 21 and add 4 here

So we get 252

Answer:

[tex]36 \times 7 = 252[/tex]

Step-by-step explanation:

Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.

Hope it helps u mate

Answer: a. $40,800 b. 36

Step-by-step explanation:

Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].

[tex]\sigma= \$14,900[/tex]

a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.

Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]

= 40,800

hence, the point estimate of the mean salary for all college graduates in this town = $40,800

b.  Since  lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.

Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]

Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.

z-value for 99% confidence level  = 2.576

So,

[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]

The sample size used for the analysis =36

Answer:

-23

Step-by-step explanation:

16x² - 106x - 105

factoring X

14 x -120 = -1680

14 - 120 = -106

16x² + 14x - 120x - 105

(16x² + 14x) -(120x - 105)

factor out 2 and -15 to get the same expression (8x + 7)

2x(8x + 7) - 15(8x + 7)

(8x + 7)(2x - 15)

a = 7

b = -15

a + 2b

7 + (-15 x 2)

7 + (-30)

= -23

Answer:

Number 1: A

Number 2:D

Step-by-step explanation:

Answer:

Hello,

Just using the theorem of Thalès,

Step-by-step explanation:

Let say h the hight of the building

[tex]\dfrac{h}{3} =\dfrac{42.75}{1.23}\\\\h=104.268296...\approx{104(m)}[/tex]

Answer:

x = 3/2

Step-by-step explanation:

4/3 ( 3x+9) -2x= 15

Distribute 4/3

4x+12 -2x =15

Combine like terms

2x+12 = 15

Subtract 12 from each side

2x+12-12 =15-12

2x = 3

Divide by 2

2x/2 = 3/2

x = 3/2

Answer:

4/3(3x+9)-2x=15

4x+12+9-2x=15

2x+21=15

2x=-6

x=-3

Let me know if this helps!

Answer:

24 and 32 ft or 32 and 24 ft

Step-by-step explanation:

Perimeter of rectangle(p)=2(l+b)

or, 112/2=l+b

Therefore, l+b=56

Now,

diagonal(d)=40

By pythogoras theorem,

h^2=p^2+b^2 (d=h here)

40^2=l^2+b^2

Now,

Square l+b=56

(l+b)^2=56^2

l^2+2lb+b^2=3136

2lb=3136-1600

lb=1536/2

Therefore, lb=768

b=768/l

Now,

Perimeter of rectangle(p)=2(l+b)

l+b=56

l+768/l=56

l^2+768=56l

l^2+768-56l=0

Factoring,

(l - 32) (l - 24) = 0

Either l= 32 or l = 24

When l=32,

l+b=56

32+b=56

b=24

When l=24

l+b=56

24+b=56

b=32

So the dimensions of the dance floor are 24 and 32 ft or 32 and 24 ft.

Answer:

24 ft x 32 ft

Step-by-step explanation:

[tex]2x+2y=112[/tex]

[tex]\sqrt{x^{2}+y^{2} } =40[/tex]

Graph the equations

Find the point where they intersect

Answer is 24 ft and 32 ft

Answer:

8[2]×88888

Step-by-step explanation:

[8×8]=8[2]×88888

Answer:

Explained below.

Step-by-step explanation:

Let X = systolic blood pressure measurements.

It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].

(a)

Compute the percentage of measurements that are between 71 and 89 as follows:

[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]

                        [tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]

The percentage is, 0.9973 × 100 = 99.73%.

Thus, the percentage of measurements that are between 71 and 89 is 99.73%.

(b)

Compute the probability that a person's blood systolic pressure measures more than 89 as follows:

[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]

                [tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]

Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.

(c)

Compute the probability that a person's blood systolic pressure being at most 75 as follows:

Apply continuity correction:

[tex]P(X\leq 75)=P(X<75-0.5)[/tex]

                [tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]

Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.

(d)

Let x be the blood pressure required.

Then,

P (X < x) = 0.15

⇒ P (Z < z) = 0.15

⇒ z = -1.04

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]

Thus, the 15% of patients are expected to have a blood pressure below 76.9.

(e)

A z-score more than 2 or less than -2 are considered as unusual.

Compute the z score for [tex]\bar x[/tex] as follows:

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

  [tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]

The z-score for the mean blood pressure measurement of 3 patients is more than 2.

Thus, it would be unusual.

Answer:

a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication

Step-by-step explanation:

a) This expression can be solved by using the Compatibility of Equality with Addition, that is:

1) [tex]3+x = 27[/tex] Given

2) [tex]x+3 = 27[/tex] Commutative property

3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition

4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property

5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction

6) [tex]x=24[/tex] Modulative property/Subtraction/Result.

b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:

1) [tex]\frac{x}{6} = 5[/tex] Given

2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division

3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication

4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property

5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse

6) [tex]x = 30[/tex] Modulative property/Result

Answer:

3 + x = 27

✔ subtraction property of equality with 3

x over 6  = 5

✔ multiplication property of equality with 6

Answer:

[tex]D = 42.5\ inch[/tex]

Step-by-step explanation:

Given

[tex]L = Length[/tex] and [tex]W = Width[/tex]

[tex]L:W = 8: 5[/tex]

[tex]Perimeter = 117[/tex]

Required

Determine the Diagonal

First, the dimension of the screen has to be calculated;

Recall that; [tex]L:W = 8: 5[/tex]

Convert to division

[tex]\frac{L}{W} = \frac{8}{5}[/tex]

Multiply both sides by W

[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]

[tex]L = \frac{8W}{5}[/tex]

The perimeter of a rectangle:

[tex]Perimeter = 2(L+W)[/tex]

Substitute [tex]L = \frac{8W}{5}[/tex]

[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]

Take LCM

[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]

[tex]Perimeter = 2(\frac{13W}{5})[/tex]

Substitute 117 for Perimeter

[tex]117 = 2(\frac{13W}{5})[/tex]

[tex]117 = \frac{26W}{5}[/tex]

Multiply both sides by [tex]\frac{5}{26}[/tex]

[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]

[tex]\frac{5 * 117}{26} = W[/tex]

[tex]\frac{585}{26} = W[/tex]

[tex]22.5 = W[/tex]

[tex]W = 22.5[/tex]

Recall that

[tex]L = \frac{8W}{5}[/tex]

[tex]L = \frac{8 * 22.5}{5}[/tex]

[tex]L = \frac{180}{5}[/tex]

[tex]L = 36[/tex]

The diagonal of a rectangle is calculated using Pythagoras theorem as thus;

[tex]D = \sqrt{L^2 + W^2}[/tex]

Substitute values for L and W

[tex]D = \sqrt{36^2 + 22.5^2}[/tex]

[tex]D = \sqrt{1296 + 506.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = 42.4529150943[/tex]

[tex]D = 42.5\ inch[/tex] (Approximated)

Answer:

Bank A spending= $20

Bank B spending= $22.5

Bank A is cheaper with $2.5

Step-by-step explanation:

Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions.

Sheade 35 transactions.

Total charges from bank A

= $20 monthly

Bank B charged a $5 monthly fee for a checking account and debit card, plus

$ 0.50 for each transaction.

She made 35 transactions.

Total charges on bank B= $5 + (0.5)35

Total charges on bank B= $5+17.5

Total charges on bank B= $22.5

Answer:

Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function

g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)?

left 13 units, down 2 units

right 13 units, down 2 units

left 13 units, up 2 units

right 13 units, up 2 units

Answer:

The portfolio beta is  [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

From the question we are told that

      The  first investment is [tex]i_1 = \$ 25,000[/tex]

       The  first  beta is  [tex]k = 0.8[/tex]

      The second investment is  [tex]i_2 = \$ 40,000[/tex]

       The  second  beta is  [tex]w = 1.7[/tex]

Generally the portfolio beta is mathematically represented as

           [tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]

substituting values

          [tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]

          [tex]\alpha = 1.354[/tex]

Answer:

2.8 < x < 5.4

Step-by-step explanation:

Given the triangle with two known sides, 4.1 and 1.3, the range of possible values of the third side, x, can be ascertained by considering the triangle inequality theorem.

According to the theorem, when you add any two of the angles in a triangle, it should give you a value greater than the third side.

If a, b, and c are 3 sides of a triangle, the theorem implies that:

a + b > c.

Therefore, a - b < c < a + b

We can use this logic to find the possibly values of x in the given triangle above.

Thus,

4.1 - 1.3 < x < 4.1 + 1.3

2.8 < x < 5.4

Range of possible sizes of x is 2.8 < x < 5.4

Answer:

No, -12 is not a solution.

Step-by-step explanation:

8u-1=6u

8(-12)-1=6(-12)

-96-1=-72

-97=-72

Untrue, to it’s not a solution

Answer:

Step-by-step explanation:

Using the value for calculating the confidence interval as given;

CI = xbar + Z*σ/√n

xbar  is the mean = 37.14+42.86/2

xbar= 80/2

xbar = 40

Z is the z-score at the 90% confidence = 1.645

σ is the standard deviation

n is the sample size = 35

Given the confidence interval CI as [37.14, 42.86]

Using  the maximum value of the confidence interval to get the value of the standard deviation, we will have;

42.86 =  xbar + Z*σ/√n

42.86 = 40 + 1.645* σ/√35

42.86-40 = 1.645*σ/√35

2.86 = 1.645*σ/√35

2.86/1.645 = σ/√35

1.739 = σ/√35

1.739 = σ/5.92

σ= 1.739*5.92

σ = 10.295

Hence, the sample standard deviation of a pair of jeans is 10.295

Answer:

Option A. 4√5

Step-by-step explanation:

To obtain the value of x, we must first obtain the value of y as shown in the attached photo.

The value of y can be obtained by using the pythagoras theory as illustrated below:

In this case y is the longest side i.e the Hypothenus.

y² = 4² + [4√3]²

y² = 4² + [4² × (√3)²]

y² = 4² + [4² × 3]

y² = 16 + [16 × 3]

y² = 16 + 48

y² = 64

Take the square root of both side

y = √64

y = 8

Finally, we shall determine the value of x by using the pythagoras theory as illustrated below.

Note: x is the longest side i.e the Hypothenus in this case.

x² = 4² + 8²

x² = 16 + 64

x² = 80

Take the square root of both side

x = √80

x = √(16 × 5)

x = √16 × √5

x = 4√5

Therefore, the value of x is 4√5.

Answer:

Step-by-step explanation:

x² + 5x - 24

To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24

That's

x² + 8x - 3x - 24

Factorize x out

That's

x( x + 8) - 3(x + 8)

Factor x + 8 out

We have the final answer as

Hope this helps you

Answer:(x-3)(x+8)

Step-by-step explanation:

Answer:

7.745

Step-by-step explanation:

Square root of 60 equals X.

Answer:

1000

Step-by-step explanation:

I guess, something went wrong with the text up there.

I assume it should say 2cm×2cm×2cm cubes. right ? because a cube has 3 dimensions, not just 2.

otherwise an infinitely large number of "just squares" would fit into the box ...

so, the box is

1m×20cm×4cm = 100cm×20cm×4cm = 8000 cm³

a single cube would be

2cm×2cm×2cm = 8 cm³

therefore,

8000 / 8 = 1000 cubes can be packed into that box, since the dimensions of the box in relation to the dimensions of the cubes do not force to have some empty left over space. the box can be packed tightly.

Answer:

Step-by-step explanation:

15-10=5 degrees

Answer:

hope this answer helps.

Answer:

To find the volume of this cube, you would have to multiply 1.08 by 5.25 by 3.3 feet. If you did this, you would get: 18.711 feet^3. This is the volume of the rectangular prism.

Hope this helped!

Answer: 56.9 years to 63.1 years.

Step-by-step explanation:

Confidence interval for population mean (when population standard deviation is unknown):

[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]

, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].

Given: n= 24

degree of freedom = n- 1= 23

[tex]\overline{x}[/tex]= 60 years

s= 7.4 years

[tex]\alpha=0.05[/tex]

Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:

[tex]t_{\alpha/2}=2.0687[/tex]

A 95% confidence interval on the true mean age:

[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]

Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.

Answer:

Step-by-step explanation:

[tex]3-(-4) \\-\times - = +\\3+4 \\=7[/tex]

Answer:

7

Step-by-step explanation:

because you when multiply -1 by -4 u get positive 4 then 3 + 4 equals 7

Answer:

2 . y=-1

Step-by-step explanation:

m=0  (it is a straight line)

use (-6,-1) in y=mx+b

-1=0(-6)+b

-1=b

equation is now

y=0(x)-1

y=-1