What is the probability of rolling a number less than or equal to 8 with the sum of two dice, given that at least one of the dice must show a 6?

Answers

Answer 1

Given that one die is a 6. So for the sum of the dice to be less than or equal to 8, the other die must be equal to or less than 2.

And the probability of roll a two or less is:

P(≤2)=2/6=1/3

Answer 2

[tex]|\Omega|=6^2=36\\ |A|=4\\\\ P(A)=\dfrac{4}{36}=\dfrac{1}{9}\approx11\%[/tex]

Related Questions

The prize of bronze has increased by 10% per year from 2000. In the year 2000, Harry bought a bronze medal for $120. Which of the following functions f(x) can be used to represent the price of the medal x years after 2000?

Answers

Hey there!

Consider the exponential growth equation:

[tex]f(x) = P(1 + r)^{t} [/tex], where:

P = initial amount
r = interest rate (as a decimal, divide a percentage by 100 to get its decimal form)
t = years

All you need to do is plug in your given numbers:

P = 120
r = 0.10
t = x

Your final equation will be:

[tex]f(x) = 120(1.10)^{x}[/tex]

Hope this helped you out! :-)

The function that should be used to represent the price of the medal x years after 2000 is [tex]f(x) = 120 (1.10)^x[/tex]

Given that,

The prize of bronze has increased by 10% per year from 2000. In the year 2000, Harry bought a bronze medal for $120.

Based on the above information, the calculation is as follows:

[tex]f(x) = P(1 + rate)^t[/tex]

Here P means $120

rate is 10%

T = x

So, it should be

[tex]f(x) = 120 (1.10)^x[/tex]

Therefore we can conclude that The function that should be used to represent the price of the medal x years after 2000 is [tex]f(x) = 120 (1.10)^x[/tex]

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The area of a rectangular wall of a barn is 168 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.

Answers

so area is 168 sq ft

That means that length * width = 168 sq ft
Since length = 10 + 2 w

we get (10+2w)(w) = 168

Multiply it out and you get 2w^2 + 10w - 168 = 0

This is a quadratic equation. You can use the formula here, but i'll just tell you the answer

w = -12, or 7
since it can't equal -12 (ever heard of a barn with a length of -12?), you figure out the answer is 7.

If the width is 7, then the length is 10+2(7) = 24.

Have a nice day!

A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. at t = 0, another brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 8 gal/min. find the amount of salt in the tank when the tank contains exactly 40 gal of solution.

Answers

Let [tex]A(t)[/tex] be the amount of salt (in lbs) in the tank at time [tex]t[/tex]. Then

[tex]\dfrac{\mathrm dA(t)}{\mathrm dt}=\dfrac{1\text{ lb}}{1\text{ gal}}\dfrac{4\text{ gal}}{1\text{ min}}-\dfrac{A(t)\text{ lbs}}{80+(4-8)t)\text{ gal}}\dfrac{8\text{ gal}}{1\text{ min}}[/tex]
[tex]\dfrac{\mathrm dA(t)}{\mathrm dt}=4-\dfrac{2A(t)}{20-t}[/tex]
[tex]\dfrac{\mathrm dA(t)}{\mathrm dt}+\dfrac{2A(t)}{20-t}=4[/tex]
[tex]\dfrac1{(20-t)^2}\dfrac{\mathrm dA(t)}{\mathrm dt}+\dfrac{2A(t)}{(20-t)^3}=\dfrac4{(20-t)^2}[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac{A(t)}{(20-t)^2}\right]=\dfrac4{(20-t)^2}[/tex]
[tex]\dfrac{A(t)}{(20-t)^2}=\dfrac4{20-t}+C[/tex]
[tex]A(t)=4(20-t)+C(20-t)^2[/tex]

Given that [tex]A(0)=\dfrac{1\text{ lb}}{8\text{ gal}}\times(80\text{ gal})=10\text{ lbs}[/tex], we have

[tex]10=4(20-0)+C(20-0)^2\implies C=-\dfrac7{40}[/tex]

so that the amount of salt in the tank is given by

[tex]A(t)=4(20-t)-\dfrac7{40}(20-t)^2[/tex]
[tex]A(t)=10+3t-\dfrac7{40}t^2[/tex]

which is valid for [tex]0\le t\le20[/tex], since the tank will be empty when [tex]80+(4-8)t=0[/tex].

The tank will contain 40 gal of solution when [tex]80+(4-8)t=40\implies t=10[/tex], at which point the amount of salt in the tank would be

[tex]A(10)=10+3(10)-\dfrac7{40}(10)^2=\dfrac{45}2=22.5\text{ lbs}[/tex]

Final answer:

To find the amount of salt when the tank contains exactly 40 gallons, create and solve differential equations for salt concentration and tank size over time. We find the tank size is 40 at 10 minutes, at which point there is approximately 14.2 lbs of salt.

Explanation:

To solve this, you need to understand that the total amount of salt at any time t is equal to the amount of salt coming in minus the amount of salt going out.

To begin with, the tank has 80 gal x 1/8 lb/gal = 10 lbs of salt.

The amount of salt coming in is 4 gal/min * 1 lb/gal = 4 lbs/min

The amount of salt going out depends on the concentration of the salt in the tank at that time. This is (4-8)(total salt/liters in tank at time t).

Setting up a differential equation and solving gives us an equation for salt concentration and volume at time t:

The equation for the tank size(in gallons) at time t (in minutes) is: tank size = 80 - 4t

The equation for the salt in tank at time t (in minutes) is: salt = 10 - 4t + 80e^-2t

When the tank size is exactly 40 gallons, tank size = 40 = 80 - 4t so t = 10 minutes

Plugging t = 10 into our equation for salt gives us: salt = 10 - 4*10 + 80e^-20 = approximately 14.2 lbs.

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If log6⁡⁡3+log6⁡⁡72=x, what is the value of x?

Answers

[tex]\bf \textit{logarithm of factors}\\\\ log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y) \\\\\\ \textit{Logarithm Change of Base Rule}\\\\ log_{{ a}}{{ b}}\implies \cfrac{log_{{ c}}{{ b}}}{log_{{ c}}{{ a}}}\\\\ -------------------------------\\\\ log_6(3)+log_6(72)=x\implies log_6(3\cdot 72)=x\implies log_6(216)=x \\\\\\ \cfrac{log(216)}{log(6)}=x\impliedby \textit{using the change of base rule}[/tex]

recall that, log <--- with no apparent base, implies base10, so you can just plug that in your calculator

for the change of base rule, it doesn't really matter what base you use, so long is the same above and below, it just so happen, that we used base10 in this case, but could have been anything, same result.

Given the geometric sequence where a1=-3 and the common ratio is 9 what is the domain for n

Answers

[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=-3\\ r=9 \end{cases}\implies a_n=-3(9)^{n-1}[/tex]

for a geometric sequence, the values "n" can take on for it to work, is usually all whole numbers, or positive integers, including 0, or you can say { x | x ∈ ℤ; x ⩾ 0 }

evaluate the surface integral:S

(x^2z + y^2z) dS
S is the hemisphere
x2 + y2 + z2 = 9, z ≥ 0

Answers

Assuming [tex]S[/tex] does not include the plane [tex]z=0[/tex], we can parameterize the region in spherical coordinates using

[tex]\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle[/tex]

where [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le\dfrac\pi/2[/tex]. We then have

[tex]x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v[/tex]
[tex](x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v[/tex]

Then the surface integral is equivalent to

[tex]\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du[/tex]

We have

[tex]\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle[/tex]
[tex]\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle[/tex]
[tex]\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle[/tex]
[tex]\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v[/tex]

So the surface integral is equivalent to

[tex]\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du[/tex]
[tex]=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv[/tex]
[tex]=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw[/tex]

where [tex]w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv[/tex].

[tex]=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}[/tex]
[tex]=\dfrac{243}2\pi[/tex]

Which equation represents the line that passes through the points (3, 7) and ( - 1, - 1)?

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 3}}\quad ,&{{ 7}})\quad % (c,d) &({{ -1}}\quad ,&{{ -1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-1-7}{-1-3}\implies \cfrac{-8}{-4}\implies 2[/tex]

[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-7=2(x-3)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-7=2x-6\implies y=2x+1[/tex]

Molly had 1/8 of a bag of birdseed. She separated it equally into 2 bird feeders. What part of a bag did each feeder get?

Answers

1/8 of a bag divided into two equal parts.
Each part gets 1/2 of 1/8, which is (1/2)*(1/8)=1/16 of a bag.
(hint: "of" frequently means multiply)

Answer: each feeder gets 1/16 of a bag of birdseed.

1/16

1/8 ÷ 2/1

1/8 × 1/2 (use the reciprocal of 2)

1×1=1
And
8×2=16

therefore each birdfeeder got 1/16 of a bag

jim is running on a trail that is 5/4 of a mile long. so far he has run 2/3 of the trail. how many miles has he run so far

Answers

(5/4) / (2/3)
= 5/6

therefore: he has run 5/6 miles so far

Write the equation 6x − 3y = −12 in the form y = mx + b.

Answers

Solve for the variable y (move the x to the right of equal with changed sign)

M is the coefficient before the x and b is the known number

-3y = -12 - 6x

Since the y can't be negative, multiply every term for -1, therefore change their sign

3y = 6x + 12

To find y, divide both terms for 3

[tex] \frac{3}{3}y = \frac{6x+12}{3} [/tex]

y = 2x+4

Therefore your answer is y = 2x+4

We did not find results for: A measure of malnutrition, called the pelidisi, varies directly as the cube root of a person's weight in grams and inversely as the person's sitting height in centimeters. A person with a pelidisi below 100 is considered to be undernourished, while a pelidisi greater than 100 indicates overfeeding. A person who weighs 48,820 g with a sitting height of 78.7 cm has a pelidisi of 100. Find the pelidisi (to the nearest whole number) of a person whose weight is 54,688 g and whose sitting height is 72.6 cm. Is this individual undernourished or overfed?The pelidsi is _____Round to the nearest integer as needed..

Answers

Since a pelidisi below ( 100 ) is considered undernourished and a pelidisi greater than ( 100 ) indicates overfeeding, with a pelidisi of ( 114 ), this individual is considered to be overfed.

Let's denote the pelidisi as ( P ), the weight in grams as ( W ), and the sitting height in centimeters as ( H). According to the given information, the pelidisi varies directly as the cube root of the person's weight and inversely as the person's sitting height. This relationship can be expressed mathematically as:

[tex]\[ P = k \times \frac{\sqrt[3]{W}}{H} \][/tex]

where ( k ) is the constant of variation.

We are given that a person with a weight of ( 48,820 ) g and a sitting height of ( 78.7 ) cm has a pelidisi of ( 100 ). We can use this information to find the value of ( k ):

[tex]\[ 100 = k \times \frac{\sqrt[3]{48820}}{78.7} \][/tex]

Solving for $ k $:

[tex]\[ k = \frac{100 \times 78.7}{\sqrt[3]{48820}} \]\[ k \approx \frac{7870}{36} \approx 218.611 \][/tex]

Now that we have the value of $ k $, we can find the pelidisi for a person with a weight of $ 54,688 $ g and a sitting height of $ 72.6 $ cm:

[tex]\[ P = 218.611 \times \frac{\sqrt[3]{54688}}{72.6} \][/tex]

Calculating $ P $:

[tex]\[ P \approx 218.611 \times \frac{38}{72.6} \]\[ P \approx 218.611 \times 0.522 \]\[ P \approx 114.14 \][/tex]

Rounded to the nearest whole number, the pelidisi of a person with a weight of ( 54,688 ) g and a sitting height of ( 72.6 ) cm is ( 114 ).

Since a pelidisi below ( 100 ) is considered undernourished and a pelidisi greater than ( 100 ) indicates overfeeding, with a pelidisi of ( 114 ), this individual is considered to be overfed.

A package of 3 pairs of insulated socks costs $25.17. What is the unit price of the pairs of socks?

Answers

The answer would be $8.38 because the price is 25.17 for three pairs so to get the unit price you just divide that by three:
25.17 / 3 = 8.39

A circle with a radius of 1/2 ft is dilated by a scale factor of 8. Which statements about the new circle are true? Check all that apply.
A.The length of the new radius will be 4 feet.
B. The length of the new radius will be 32 feet.
C.The new circumference will be 8 times the original circumference.
D.The new circumference will be 64 times the original circumference.
E.The new area will be 8 times the original area.
F.The new area will be 64 times the original area.
G.The new circumference will 8PI be
H.The new area will be 16PI square feet.

Answers

Answer:

The statements A,C,F,G and H are true.

Step-by-step explanation:

It is given that the radius of circle before dilation is [tex]\frac{1}{2}ft[/tex] and the scale factor is 8.

The circumference of original circle is,

[tex]S_1=2\pi r[/tex]

[tex]S_1=2\pi \times \frac{1}{2}=\pi[/tex]

The area of original circle is,

[tex]A_1=\pi r^2[/tex]

[tex]A_1=\pi (\frac{1}{2})^2[/tex]

[tex]A_1=\frac{\pi}{4}[/tex]

The dilation by scale factor 8 means the radius of new circle is 8 times of the original circle.

[tex]r=8\times \frac{1}{2}[/tex]

Therefore the radius of new circle is 4 ft and the statement A is true.

The circumference of original circle is,

[tex]S_2=2\pi r[/tex]

[tex]S_2=2\pi \times 4=8\pi[/tex]

[tex]\frac{S_2}{S_1}=\frac{8\pi}{\pi} =8[/tex]

The new circumference will be 8 times the original circumference. The statement C is true.

The area of original circle is,

[tex]A_2=\pi r^2[/tex]

[tex]A_2=\pi (4)^2[/tex]

[tex]A_2=16\pi[/tex]

[tex]\frac{A_2}{A_1}=\frac{16\pi}{\frac{\pi}{4}}=64[/tex]

The new area will be 64 times the original area. Therefore statement F is true.

The new circumference will [tex]8\pi[/tex],The new area will be [tex]16\pi[/tex] square feet.

solve for a in terms of F and m: F=ma

Answers

To solve for a, you must get a by itself on one side of the equation. Now, a is "joined" to m by multiplication. To "separate" them, use the inverse operation, division.

Divide both sides of the equation by m.

[tex]F=ma \\ \frac{F}{m}=\frac{ma}{m} \\ \frac{F}{m}=a \\ a=\frac{F}{m}[/tex]

To find acceleration 'a' in the equation F = ma, divide both sides by mass 'm', resulting in the formula [tex]a =\frac{f}{m}[/tex]

To solve for a in terms of F and m from the equation F = ma,

where F represents force,

m represents mass,

and a represents acceleration,

we need to isolate the variable a.

[tex]f= m*a\\a =\frac{f}{m}[/tex]

This gives us the formula:

[tex]a =\frac{f}{m}[/tex]

This formula tells us that the acceleration of an object is equal to the force applied to it divided by its mass.

Solve the equation. show work. check your answer. 4y + 5 = - 31

Answers

4y+5=-31
4y=-31-5
4y=-36
y=-9

Our goal with this equation is to solve for y by simplifying the equation.

4y + 5 = -31
Our first step is to always get 4y by itself.
To do so, we need to subtract 5. However, when you perform any order of operations (except for distribution) you need to do it to both sides.

So, let's subtract 5 from both sides.
5 - 5 = 0
-31 -5 = -36

We're now left with:
4y = -36.

Now we must simplify for y- divide both sides by 4.
4y / 4 = y
-36 / 4 = -9 (When you divide a negative by a positive, you will result with a negative)

We are now left with:
y = -9.
This is your solution.

I hope this helps!

A group of 11 friends ordered four pizzas to share. They divided the pizzas up evenly and all ate the same amount. Express in decimal form the proportion of a pizza that each friend ate.

Answers

4/11, 4 pies per person = 0.363636 - repeating

Final answer:

Each friend ate approximately 0.3636 of a pizza when the four pizzas were divided evenly among 11 friends.

Explanation:

The student's question involves dividing four pizzas evenly among 11 friends, so each person gets the same proportion of pizza. We need to convert this proportion into decimal form to answer the question.

To find the proportion of a pizza that each friend ate, we calculate 4 pizzas ÷ 11 friends. So, each friend ate ≈ 0.3636 of a pizza. We arrived at this by dividing 4 by 11, which yields a repeating decimal, so we round it to four decimal places to express it accurately.

This value represents the proportion of pizza each person ate when the pizzas were divided equally.

The dimension of a rectangular pool are 24.5 feet by 13 feet. The depth of the water is 4 feet. Each cubic foot contains 7.48 gallons of water. How many gallons of water to the nearest tenth, are needed to fill the pool to 80% capacity

Answers

Answer:

Pool needed to be filled = 7623.62 gallons

Step-by-step explanation:

Length of rectangular pool = 24.5 feet

Width of rectangular pool = 13 feet

Depth of rectangular pool = 4 feet

Now, Volume of the pool = Length × Width × Depth

= 24.5 × 13 × 4

= 1274 cubic feet

Now, 1 cubic feet = 7.48 gallons

⇒ 1274 cubic feet = 7.48 × 1274

= 9529.52 gallons

So, Volume of the pool = 9529.52 gallons

Now, the pool is to be filled 80%

So, Pool needed to be filled = 9529.52 × 0.80

= 7623.62 gallons

The number of gallons of water to the nearest tenth, that are needed to fill the pool to 80% capacity is 7623.6 gallons.

Number of gallons of water

First step:

Volume of the pool=Length × Width × Depth

Volume of the pool= 24.5 ft × 13ft × 4ft

Volume of the pool=1274 cubic feet

Second step:

Number of gallons=(7.48 × 1274)×80%

Number of gallons=9529.5 gallons×80%

Number of gallons=7623.6 gallons

Inconclusion the number of gallons of water to the nearest tenth, that are needed to fill the pool to 80% capacity is 7623.6 gallons.

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A line passes through (−2,7) and (3,2). Find the slope-intercept form of the equation of the line. Then fill in the value of the slope, m, and the value of the y-intercept

Answers

The form will be y = mx + b, where m is the slope, b is the y-intercept

m = (2-7) / (3+2) = -1

b = 3 +2 = 5

So y = -x + 5

Final answer:

The equation of line passing through points (-2,7) and (3,2) is y = -x + 5. The slope, m, is -1. The y-intercept, b, is 5.

Explanation:

The subject matter here is finding the equation of a line in slope-intercept form, which is expressed as y = mx + b. Here, 'm' is the slope of the line and 'b' is the y-intercept. The slope, m, can be found using the formula: m = (y2 - y1)/(x2 - x1). Applying the coordinates given, (-2,7) and (3,2), we find the slope, m = (2 - 7) / (3 - (-2)) = -5 / 5 = -1.

Then, substituting m, x, and y into the equation, we get the y-intercept. Using the point (-2,7), we have: 7 = -1*-2 + b -> 7 = 2 + b -> b = 7 - 2 = 5. So the y-intercept, b, is 5. Therefore, the equation of the line in slope-intercept form is y = -x + 5.

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"if a snowball melts so that its surface area decreases at a rate of 1 cm 2 min, find the rate at which the diameter decreases when the diameter is 10 cm." (stewart 249) stewart, james. single variable calculus, 8th edition. cengage learning, 20150101. vitalbook file.

Answers

We need to find the rate of the diameter, which we can denote as d(d)/dt.

[tex]\frac{dA}{dt} = \frac{dA}{dx} \cdot \frac{dr}{dt}[/tex]
[tex]\frac{dA}{dt} = -1[/tex], since it is decreasing.

[tex]-1 = \frac{dA}{dr} \cdot \frac{dr}{dt}[/tex]

[tex]A = 4\pi \cdot r^{2}[/tex]
[tex]\frac{dA}{dr} = 8\pi \cdot r[/tex]

At r = 5:
[tex]\frac{dA}{dr} = 40 \pi[/tex]

[tex]\frac{dr}{dt} = -\frac{1}{40 \pi}[/tex]

Since the diameter is twice the radius and this is simply the rate at which the radius is decreasing, then the diameter will be decreasing twice as fast:

[tex]\frac{d(d)}{dt} = -\frac{1}{20\pi}[/tex]

Thus, the diameter is decreasing at a rate of 1/(20pi) cm/min.

In a right triangle, angle C measures 40°. The hypotenuse of the triangle is 10 inches long. What is the approximate length of the side adjacent to angle C?
6.4 inches
7.7 inches
8.4 inches
13.1 inches

Answers

Answer

Find out the what is the approximate length of the side adjacent to angle C .

To prove

As given

In a right triangle, angle C measures 40°.

The hypotenuse of the triangle is 10 inches long.

Than by using the trignometric identity

[tex]cos\angle C= \frac{Base}{Hypotenuse}\\cos\angle C= \frac{BC}{AC}[/tex]

As shown the diagram is given below

AC= 10 inches , ∠C = 40 °

cos 40 = 0.766 (approx)

Put in the above formula

0.766 × 10 = BC

7.66 = BC

7.7 inches (approx) = BC

Option (b) is correct .

The correct option is Option C [tex]\boxed{{\mathbf{7}}{\mathbf{.66 inches}}}[/tex] .

Further explanation:

The cosine ratio can be represented as,

[tex]\cos \theta = \frac{{{\text{base}}}}{{{\text{hypotenuse}}}}[/tex]

Here, base is the length of the side adjacent to angle [tex]\theta[/tex] and hypotenuse is the longest side of the right angle triangle.

The length of side opposite to angle [tex]\theta[/tex] is perpendicular that is used for the sine ratio.

Step by step explanation:

Step 1:

From the given information, the observed right angle is attached.

First find the hypotenuse and the base of the right angle triangle.

It can be seen from the attached figure that the side [tex]BC[/tex] is adjacent to angle [tex]C[/tex] and the side [tex]AC[/tex] is the hypotenuse of triangle.

Thus, the [tex]{\text{base}}=BC[/tex] and [tex]{\text{hypotenuse}}=10[/tex] .

Step 2:

We know that the cosine ratio is [tex]\cos \theta =\frac{{{\text{base}}}}{{{\text{hypotenuse}}}}[/tex] .

Therefore, it can be written as,

[tex]\cos \theta=\frac{{BC}}{{AC}}[/tex]

Now substitute the value [tex]BC=x[/tex] and [tex]{\text{AC}}=10[/tex] in the cosine ratio.

[tex]\begin{aligned}\cos C&=\frac{x}{{10}}\\{\text{co}}s40&=\frac{x}{{10}}\\0.766&=\frac{x}{{10}}\\x&=7.66\\\end{aligned}[/tex]

Therefore, the approximate length of the side adjacent to angle [tex]C[/tex] is [tex]7.7{\text{ inches}}[/tex] .

Thus, option C is correct.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Trigonometry

Keywords: Distance, Pythagoras theorem, base, perpendicular, hypotenuse, right angle triangle, units, squares, sum, cosine ratio, adjacent side to angle, opposite side to angle.

The sum of two consecutive terms in the arithmetic sequence 3, 6, 9, 12, ... is 303; find these two terms.
The first consecutive term of the arithmetic sequence is ?
The second consecutive term of the arithmetic sequence is ?

Answers

1st consecutive term is x. 2nd consecutive term is (x + 3)
x + x + 3 = 303
2x + 3 = 303
2x = 303 - 3
2x = 300
x = 300/2
x = 150

x + 3 = 150 + 3 = 153

so ur 2 numbers are 150 and 153

Final answer:

The first consecutive term of the arithmetic sequence that sums to 303 is 150. The second consecutive term is 153. We found this by setting up an equation for the sum of two consecutive terms and solving for the first term.

Explanation:

To find the two consecutive terms in the arithmetic sequence 3, 6, 9, 12, ... that sum up to 303, we first need to understand the properties of an arithmetic sequence. The given sequence has a common difference of 3 (that is, each term is 3 more than the previous term). Let's denote the first of these two consecutive terms as a. Therefore, the next term would be a + 3 (since the common difference is 3).

We are given that the sum of these two terms is 303, so we can write an equation:

a + (a + 3) = 303

Combining like terms, we get:

2a + 3 = 303

Subtracting 3 from both sides gives:

2a = 300

Dividing both sides by 2 gives:

a = 150

So, the first term is 150 and the second term, being a + 3, is 153.

What is the rate of growth as a percent for 23(1.0032)

Answers

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ \textit{so let's see the amount in the parentheses}\\\\ 1.0032\implies 1+\underline{0.0032}\impliedby \frac{r}{100} \\\\\\ thus\qquad 0.0032=\cfrac{r}{100}\implies 100\cdot 0.0032=r\implies 0.32\%=r[/tex]

A man invests
$3700
in three accounts that pay
5%,
6%
, and
7%
in annual interest, respectively. He has
3
times as much invested at
7%
than he does at
5%
. If his total interest for the year is
$234
, how much is invested at each rate?

Answers

First account $3700 at 7% Interest annually = $259.00
Second account $3700 at 6% interest annually = $222.00
Thirs account $3700 at 5% interest annually = $185.00

He has 3 times as much invested at 7% than he does at 5%.
If his total interest for the year is $234, how much is invested at each rate?
Doesn't make any sense - please rephrase.

Calculate the slope m, if defined, of the straight line through the given pair of points. Try to do the problem without writing anything down except the answer. (If an answer is undefined, enter UNDEFINED.) (6, 5) and (7, 2)

Answers

m is defined as rise over run. Here the rise is 2-5 and the run is 7-6, so the slope is -3/1 = -3. Could you do this problem in your head?

The slope m of the straight line through the points (6, 5) and (7, 2) is -3.

What is a slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

The slope of the line is defined as the ratio of the rise to the run.

To find the slope, we can use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (6, 5) and (x₂, y₂) = (7, 2).

Substituting these values, we get:

m = (2 - 5) / (7 - 6) = -3 / 1 = -3

Therefore, the slope of the straight line through the given pair of points is -3.

To know more about slope follow

https://brainly.com/question/3493733

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You have two exponential functions. One function has the formula g(x) = 5 x . The other function has the formula h(x) = 5-x . Which option below gives formula for k(x) = (g - h)(x)?

Answers

given the exponential functions [tex]g(x)= 5^{x} [/tex] and [tex]h(x)= 5^{-x} [/tex]

[tex]k(x)=(g-h)(x)[/tex]
[tex]k(x)=g(x)-h(x) [/tex]
[tex]k(x)= 5^{x} - 5^{-x} [/tex]
[tex]k(x)= 5^{x} - \frac{1}{ 5^{x} } [/tex]
[tex]k(x)= \frac{ 5^{x} 5^{x} }{ 5^{x} } - \frac{1}{ 5^{x} } [/tex]
[tex]k(x)= \frac{ 5^{2x} }{ 5^{x} } - \frac{1}{ 5^{x} } [/tex]
[tex]k(x)= \frac{ 5^{2x}-1 }{ 5^{x} } [/tex]

Answer:

The value of [tex]k(x)=\frac{5^{2x}-1}{5^x}[/tex]

Step-by-step explanation:

We have given two function [tex]g(x)=5^x\text{and}h(x)=5^{-x}[/tex]

We have to find k(x)=(g-h)(x)

[tex]k(x)=g(x)-h(x)[/tex] (1)

We will substitute the values in equation (1) we will get

[tex]k(x)=5^x-(5^{-x})[/tex]

Now, open the parenthesis on right hand side of equation we will get

[tex]k(x)=5^x-5^{-x}[/tex]

Using [tex]x^{-a}=\frac{1}{x^a}[/tex]

[tex]k(x)=5^x-\frac{1}{5^x}[/tex]

Now, taking LCM which is [tex]5^x[/tex] we will get after simplification

[tex]k(x)=\frac{5^{2x}-1}{5^x}[/tex]

Hence, the value of [tex]k(x)=\frac{5^{2x}-1}{5^x}[/tex]

if a number is a whole number then it cannot be.......

a...an irrational number
b...a natural number
c...an integer
d...a rational number

Answers

Using number sets, it is found that a whole number cannot be irrational, hence option a is correct.

What are rational and irrational numbers?All numbers that can be represented by fractions are rational.Numbers that cannot be represented by fractions, such as non-repeating decimals and the square roots of numbers that are not perfect squares are irrational.

In this problem, any whole number can be represented by a fraction, hence it cannot be irrational and option a is correct.

More can be learned about rational and irrational numbers at https://brainly.com/question/10814303

Answer:

A. An Irrational Number

Step-by-step explanation:

Irrational numbers are numbers like pi or angles with degrees, while whole numbers are numbers from 0+

Hope it helped!

A mule deer can run 1/4 of a mile in 25 seconds. At this rate which expression can be used to determine how fast a mule deer runs in miles per hour

Answers

Ok so this might be a bit confusing but I hope u understand it. Because the problem is in seconds, I tried to stick to seconds. In an hour there are 60 minutes and in those 60 minutes there are 3,600 seconds. Now in 25 seconds the mule deer can run 1/4 mile. So think for a second how many seconds it would take for it run a full mile. If u do the math then u would get 25*4 which is 100 seconds to run a full mile. Going back to our 3,600 seconds, all u have to do is divide it by 100 to get the miles. So 3,600/100 is 36. The mile deer runs 36 miles in an hour. I hope this was of help to u

The height of a right cylinder is 3 times the radius of e base. The volume of the cylinder is 24π cubic units. What is the height of the cylinder?
A. 2 units
B.4 units
C.6 units
D. 8 units

Answers

Volume = pi * r^2 * h
h = 3r
pi * r^2 * (3r) = 24 pi
3r^3 = 24
r^3 = 8
r = 2

Height = 3*2 = 6 units

The following table shows the probability distribution for a discrete random variable.
X 13| 16 |17| 21| 23| 25 |26 |31
P(X) 0.07 |0.21| 0.17| 0.25| 0.05| 0.04| 0.13| 0.08
What is the mean of this discrete random variable. That is, what is E(X), the expected value of X?

Answers

X    | 13 |    16 | 17|    21|    23|    25 | 26 | 31| |
------------|-----------------------------------------------------------------|.
P(X) | 0.07 | 0.21| 0.17| 0.25| 0.05| 0.04| 0.13| 0.08 |
------------|-----------------------------------------------------------------|
X.P(X)    | 0.91 | 3.36| 2.89| 5.25| 1.15| 1.00| 3.38| 2.48 |
------------|-----------------------------------------------------------------|

E(X) = ∑(X.P(X) =(0.91+3.36+2.89+ 5.25+ 1.15+ 1.00+ 3.38+ 2.48)

E(X) = ∑(X.P(X) = 20.42

Pls review the calculation to be on the safe side

Answer: APEX- 20.42

Step-by-step explanation: Multiply 13 by 0.07, multiply 16 by 0.21, and so on. then add up all of the decimals and that is your answer

The two lines, X and Y, are graphed below:

Line X is drawn by joining ordered pairs negative 3,12 and 7,negative 16. Line Y is drawn by joining ordered pairs 0, negative 14 and 11, 8

Determine the solution and the reasoning that justifies the solution to the systems of equations.

(2, 7), because this point is true for both the equations

(4, −6), because this point lies only on one of the two lines

(4, −6), because this point makes both the equations true

(2, 7), because the lines intersect the x-axis at these points

Answers

consider line X.

(-3, 12), (7, -16) are 21 points on this line, so by the 2-point form of the equation of a line, the equation of X is given as follows:

[tex] \frac{12-(-16)}{-3-7}= \frac{y-12}{x-(-3)} [/tex]

[tex]\frac{28}{-10}= \frac{y-12}{x+3} [/tex]

[tex]28(x+3)=-10(y-12)[/tex]

[tex]28x+84=-10y+120[/tex]

[tex]28x+10y-36=0[/tex], divide by 2 to simplify:

[tex]14x+5y-18=0[/tex]

similarly, the equation of Y is found using the points (0, -14) and (11, 8):

[tex] \frac{-14-8}{0-11}= \frac{y-(-14)}{x-0} [/tex]

[tex] \frac{-22}{-11}= \frac{y+14}{x} [/tex]

[tex]2= \frac{y+14}{x} [/tex]

[tex]2x-y-14=0[/tex]

so y=2x-14,

substitute y=2x-14 in 14x+5y-18=0:

14x+5y-18=0

14x+5(2x-14)-18=0

14x+10x-70-18=0

24x=88

x=3.667, then y=2x-14=2*3.667-14=-6.66

the intersection point is (3.667, -6.66), it is the only point which satisfies the equations of the lines, that were found.

Answer: (4, −6), because this point makes both the equations true

Answer:c

Step-by-step explanation:

(4,-6), because this point makes both the equations true.

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