Someone please help me with this question! How can I prove it?

The answer is t ≤ 11.

Answer:

[tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

1) Convert [tex]4\frac{1}{3}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].

[tex]\frac{4\times3+1}{3} -1\frac{2}{3}[/tex]

2) Simplify 4 * 3 to 12.

[tex]\frac{12+1}{3}[/tex]

3) Simplify 12 + 1 to 13.

[tex]\frac{13}{3} -1\frac{2}{3}[/tex]

4) Convert [tex]1\frac{2}{3}[/tex]   to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].

[tex]\frac{13}{3} -\frac{1\times3+2}{3}[/tex]

5) Simplify 1 * 3 to 3.

[tex]\frac{13}{3} -\frac{3+2}{3}[/tex]

6) Simplify 3 + 2 to 5.

[tex]\frac{13}{3} -\frac{5}{3}[/tex]

7) Join the denominators.

[tex]\frac{13-5}{3}[/tex]

8) Simplify.

[tex]\frac{8}{3}[/tex]

9) Convert to mixed fraction.

[tex]2\frac{2}{3}[/tex]

(Decimal Form: 2.666667)

Thank you,
Eddie

The margin of error is 1.9%. and the interval that likely contains the true percent of all people who work out 3 or more days a week is: (71.1%, 74.9%)

Margin of error is the critical value (t score or z score) multiplied by the standard error (standard deviation of the sample). Thus;

ME = Critical value × S.E

Since n > 30, we can use the z-score as the critical value.

Assuming 95% confidence level, then z = 1.96

The standard error for a proportion is given by the formula:

s = √(p (1 − p) / n)

We are given;

p = 0.73

n = 2035:

Thus;

s = √(0.73 (1 − 0.73) / 2035)

s = 0.0098

Thus, the margin of error is:

ME = 1.96 × 0.0098

ME = 0.019

The margin of error is 1.9%.  

The interval that likely contains the true percent of all people who work out 3 or more days a week is:

73% ± 1.9% = (71.1%, 74.9%)

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Answer:

Step-by-step explanation:

If two triangles are similar, their corresponding sides will be k times greater or smaller, where k is the scale factor.

We have two corresponding sides given, 6 and 24 or 6k. Using this info, find the value of k:

The other sides of the larger triangle are:

The perimeter is the sum of sides:

Answer:

y = 33

Step-by-step explanation:

Angle y and 33 are alternate interior angles since the figure is a parallelogram and alternate interior angles are equal

y = 33

Answer:

y = 33°

Step-by-step explanation:

The diagonal of the parallelogram (a transversal) intersects two opposite and parallel sides of the parallelogram  

Then

The angles of measures y° and 33° are Alternate interior angles

Then

they are congruent.

In other words , y = 33°

The equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.

To find the equation of a line, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the given point on the line and m is the slope.

In this case, the given point is (-5, -7) and the slope is 2/5. Substituting these values into the equation, we have:

y - (-7) = (2/5)(x - (-5)).

Simplifying further:

y + 7 = (2/5)(x + 5).

Distributing the 2/5:

y + 7 = (2/5)x + 2.

Subtracting 7 from both sides:

y = (2/5)x - 5.

Therefore, the equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.

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Answer:

8+8+12+5= 33

Step-by-step explanation:

8+8+12+5=33

Answer:

a. 400

b. 4$

Step-by-step explanation:

2$ equals 0 Quantity

3$ equals 100 Quantity

4$ equals 200 Quantity

We can see that starting from 2$, a dollar will increase the Quantity by 100

The amplitude of function f(x)=cos(2x) is 1 and the period is 2.

Given that the function of x is f(x)=cos(2x).

We are required to find the value of amplitude and period of function f(x) which is given in the question.

Amplitude basically refers to maximum displacement from the equilibrium that an object in periodic motion show. It is a product analytics platform or term that helps businesses to track visitors with the help of collaborative analytics.

Period is basically the time interval between two waves. A function  that repeats its values at regular intervals or periods is known as periodic function.

The amplitude of f(x)=cos(2x) is 1 because the highest value that cos Θ can give 1. We can also see in graph that the value of cos 2x is going to 1 and starts decreasing again.

The period of f(x) is 2. From the graph we can say that the vertical distance between upper point and lower point is 2.

Hence the amplitude of function f(x)=cos(2x) is 1 and the period is 2.

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The  profit function is R(x) = -0.5 (x - 50²) + 1150

Note that:

1. Profit  = Revenue - cost

P (x) =  0.5 ( x - 90²) + 4050 - 40x - 100  

= 0.5 ( x² - 180 + 8100 + 4050 - 40x - 100  

=0.5 x² - 50x - 100  

=0.5( x² - 100x) - 100  

=  -0.5 (x - 50²) + 1150

2.  Since the minimum unit is 50.

Then   x ≤ 150

X = describe the item so it need to be a negative number

Hence the domain of P(x)  is:  0 ≤ x ≤ 150

3. Assume x = 50 , 60

R(50) = 1150 , R (60 ) = -0.5 (60-50)² + 1150 = 1100

4. R (x) = -0.5 (x-50)² + 1150  then 50 more unit is removed hence, Profit when producing 60 items =  1100

Therefore, The  profit function is R(x) = -0.5 (x - 50²) + 1150

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The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

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If a kite is flying 95 ft. off the ground, and its string is pulled taut. The angle of elevation of the kite is 59 degrees. Then the length of the string will be 110.8 ft.

Given information constitutes the following,

The distance of the flying kite from the ground, length AB (refer the figure) = 95 ft.

The angle of elevation of the kite, ∠ACB = 59°

We have to find the length of the string, that is the length AC. For that, we can apply Trigonometry as shown in the next steps of the solution.

In ΔABC, as shown in the attached figure,

sin (∠ACB ) = AB / AC

⇒ sin (59°) = 95 / AC

0.8572 = 95 / AC

AC = 95 / 0.8572

AC = 110.814

AC ≈ 110.8 ft.                [After rounding off to the nearest tenth]

Hence, the length of the string comes out to be 110.8 ft.

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To estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T = R

825 + 0.06x = 1350 + 0.02x

Simplifying the equation, we get

x = 13125

We require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

For this case, we can assume that the total salary for Teresa T is given by T = 825 + 0.06x

Where x represents the number of sales. And similarly the total salary of Ramon we have:

R = 1350 + 0.02x

We want to estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T= R

825 + 0.06x = 1350 + 0.02x

Multiply both sides by 100

[tex]$825 \cdot 100+0.06 x \cdot 100=1350 \cdot 100+0.02 x \cdot 100$[/tex]

82500 + 6x = 135000 + 2 x

Subtract 82500 from both sides

82500 + 6x - 82500 = 135000 + 2x - 82500

6x = 2x + 52500

Subtract 2x from both sides

6x - 2x = 2x + 52500 - 2x

4x = 52500

Divide both sides by 4

[tex]$\frac{4 x}{4}=\frac{52500}{4}$[/tex]

x = 13125

So then we require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

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Answer:

4 inches

Step-by-step explanation:

large rectangle - 18:12 ratio = 3:2

small rectangle - 6:4 = 3:2

Answer: 15/2 or 7.5

Step-by-step explanation:

2/3x = 5

5 divided by 2/3 or 5 x 3/2

= 15/2 or 7.5

Answer: 15/2

Step-by-step explanation:

[tex]\frac{2}{3} x-1=4\\\\\frac{2}{3}x=5\\ \\x=5(\frac{3}{2})\\\\x=\frac{15}{2}[/tex]

The period of [tex]f(x)[/tex] is [tex]\boxed{2\pi}[/tex].

Recall that [tex]\sin(x)[/tex] and [tex]\cos(x)[/tex] both have periods of [tex]2\pi[/tex]. This means

[tex]\sin(x + 2\pi) = \sin(x)[/tex]

[tex]\cos(x + 2\pi) = \cos(x)[/tex]

Replacing [tex]x[/tex] with [tex]3x[/tex], we have

[tex]\sin(3x + 2\pi) = \sin\left(3 \left(x + \dfrac{2\pi}3\right)\right) = \sin(3x)[/tex]

In other words, if we change [tex]x[/tex] by some multiple of [tex]\frac{2\pi}3[/tex], we end up with the same output. So [tex]\sin(3x)[/tex] has period [tex]\frac{2\pi}3[/tex].

Similarly, [tex]\cos(5x)[/tex] has a period of [tex]\frac{2\pi}5[/tex],

[tex]\cos(5x + 2\pi) = \cos\left(5 \left(x + \dfrac{2\pi}5\right)\right) = \cos(5x)[/tex]

We want to find the period [tex]p[/tex] of [tex]f(x)[/tex], such that

[tex]f(x + p) = f(x)[/tex]

[tex] \implies \sin(3x + p) + \cos(5x + p) = \sin(3x) + \cos(5x)[/tex]

On the left side, we have

[tex]\sin(3x + p) = \sin(3x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \sin(3x+2\pi) \cos(p-2\pi) + \cos(3x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \sin(3x) \cos(p-2\pi) + \cos(3x) \sin(p - 2\pi)[/tex]

and

[tex]\cos(5x + p) = \cos(5x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \cos(5x+2\pi) \cos(p-2\pi) - \sin(5x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \cos(5x) \cos(p-2\pi) - \sin(5x) \sin(p-2\pi)[/tex]

So, in terms of its period, we have

[tex]f(x) = \sin(3x) \cos(p - 2\pi) + \cos(3x) \sin(p - 2\pi) \\\\ ~~~~~~~~ ~~~~+ \cos(5x) \cos(p - 2\pi) - \sin(5x) \sin(p - 2\pi)[/tex]

and we need to find the smallest positive [tex]p[/tex] such that

[tex]\begin{cases} \cos(p - 2\pi) = 1 \\ \sin(p - 2\pi) = 0 \end{cases}[/tex]

which points to [tex]p=2\pi[/tex], since

[tex]\cos(2\pi-2\pi) = \cos(0) = 1[/tex]

[tex]\sin(2\pi - 2\pi) = \sin(0) = 0[/tex]

Applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.

In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.

In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.

According to the congruent chords theorem, NS = PS, thus:

8 = 2x - 6

8 + 6 = 2x

14 = 2x

Divide both sides by 2

14/2 = 2x/2

7 = x

x = 7

LP = 1/2(12)

LP = 6 units.

In summary, applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

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Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time

Answer: B) m∠3 + m∠5 = 180°

Step-by-step explanation:

Concept:

For this question, we will be looking at each answer choice and eliminating the incorrect ones

A) ∠1 ≅ ∠6

∠1 is an exterior angle

∠6 is an interior angle

They are in an alternative position

Since they are neither both exterior nor interior, they are not congruent

[tex]\large\boxed{FALSE}[/tex]

B) m∠3 + m∠5 = 180°

∠3 is an interior angle

∠5 is an interior angle

They are in a same-side position

Since they are both interiors, they fulfill the same-side interior angle theorem, which states: that if a transversal cuts two parallel lines, then the interior angles on the same side of the transversal are supplementary, which means their sum adds up to 180°.

[tex]\Huge\boxed{TRUE}[/tex]

C) m∠2 + m∠6 = 180°

∠2 is an exterior angle

∠6 is an interior angle

They are in a same-side position

Since they are on the same side, they fulfill the corresponding angle theorem which states: the angles that occupy the same relative position at each intersection are congruent to each other.

However, they are only congruent, they don't add up to 180°

[tex]\large\boxed{FALSE}[/tex]

D) ∠4 ≅ ∠8

∠4 is an interior angle

∠8 is an exterior angle

They are in an alternative position

Since they are neither both exterior nor interior, they are not congruent

[tex]\large\boxed{FALSE}[/tex]

Hope this helps!! :)

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The mean average of push ups Sasha does in 5 days is 26.2.

Mean average = Total push ups done / number of days

= (22 + 36 + 21 + 25 + 27) / 5

= 131 / 5

= 26.2

Therefore, the mean average of push ups Sasha does in 5 days is 26.2.

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The measure of the central angle is 290 degrees

The measure of arc GI is given as:

mGI = 145 degrees

The measure of the central angle is calculated as:

Central angle = 2 * mGI

Substitute the known values in the above equation

Central angle = 2 * 145

Evaluate the product

Central angle = 290

Hence, the measure of the central angle is 290 degrees

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[tex]x^3[/tex] is strictly increasing on [0, 5], so

[tex]\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125[/tex]

and

[tex]\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0[/tex]

so the integral is bounded between

[tex]\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}[/tex]

ANSWER: 480 out of 1200 were taken at the Honolulu Zoo.

Answer:

y=(−2)x−-6

Step-by-step explanation:

Use the slope −2 and the point (−5,4) to find the y-intercept.

y=mx+b

⇒4=(−2×−5)+b

⇒−4=10+b

⇒b=−6

Write the equation in slope intercept form as:

y=mx+b

⇒y=(−2)x−-6

The answer to these questions are

How to find the point where the distribution lies at 99.7%. The data is 3 sd from mean

Hence

39 - 3*(5) = 24

39 + 3*(5) = 54

The widget lies between 24 and 54

c. P(29.0 < x < 54.0)

= 29 - 39 / 5 and 54 - 39 / 5

= -2.0 and 3.0

We have to find P(Z < 3.0) - P(Z < -2.0)

= 0.9987 - 0.0228

= 97.59%

d. x = 44

= 44 - 39/ 5

= 1

We are to find P(z < 1.0)  = 84.13%

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Answer: [tex]\Large\boxed{x=-\frac{4}{5} }[/tex]

Step-by-step explanation:

Given equation

[tex]-9+log_{4}(-5x)=-8[/tex]

Add 9 on both sides

[tex]-9+log_{4}(-5x)+9=-8+9[/tex]

[tex]log_{4}(-5x)=1[/tex]

Simplify the logarithm

[tex]-5x=4^1[/tex]

[tex]-5x=4[/tex]

Divide -5 on both sides

[tex]-5x\div-5=4\div-5[/tex]

[tex]\Large\boxed{x=-\frac{4}{5} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Solving a system of equations we will see that Hari has 800 and Ram has 600.

Let's define the variables:

We know that:

(2/3)*R = (1/2)*H

We also know that in total they have 1400, then:

R + H = 1400.

So we have the system of equations:

(2/3)*R = (1/2)*H

R + H = 1400.

In the first equation we can isolate R.

R = (3/2)*(1/2)*H = (3/4)*H

Now we can replace that in the other equation:

(3/4)*H + H  =1400

H*(7/4) = 1400

H = (4/7)*1400 = 800

So Hari has 800, and:

R + H = 1400

R = 1400 - H = 1400 - 800 = 600

Hari has 800 and Ram has 600.

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