Answer:
Option d: n = 36, p = 0.97, x = 36.
Step-by-step explanation:
We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.
We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.
Let X = Number of cans that are properly filled
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]
where, n = number of trials (samples) taken = 36 cans
x = number of success = all cans are properly filled = 36
p = probabilitiy of success which in our question is probability that
can have the correct amount, i.e. p = 97%
So, X ~ Binom (n = 36, p = 0.97)
Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.
Find the centroid of the quarter of the unit circle lying in the fourth quadrant.
Step-by-step explanation:
In the fourth quadrant, the equation of the unit circle is:
y = -√(1 − x²), 0 ≤ x ≤ 1
The x and y coordinates of the centroid are:
cₓ = (∫ x dA) / A = (∫ xy dx) / A
cᵧ = (∫ y dA) / A = (∫ ½ y² dx) / A
For a quarter circle in the fourth quadrant, A = -π/4.
Solving each integral:
∫₀¹ xy dx
= ∫₀¹ -x √(1 − x²) dx
= ½ ∫₀¹ -2x √(1 − x²) dx
If u = 1 − x², then du = -2x dx.
When x = 0, u = 1. When x = 1, u = 0.
= ½ ∫₁⁰ √u du
= ½ ∫₁⁰ u^½ du
= ½ (⅔ u^³/₂) |₁⁰
= (⅓ u√u) |₁⁰
= 0 − ⅓
= -⅓
∫₀¹ ½ y² dx
= ½ ∫₀¹ (1 − x²) dx
= ½ (x − ⅓ x³) |₀¹
= ½ [(1 − ⅓) − (0 − 0)]
= ⅓
Therefore, the x and y coordinates of the centroid are:
cₓ = (-⅓) / (-π/4) = 4/(3π)
cᵧ = (⅓) / (-π/4) = -4/(3π)
Now find the product (2+ sqrt 5)(2- sqrt 5). The product is ...
the answer is -1
Answer:
-1
Step-by-step explanation:
Thanks
The product of expression (2 + √5) (2 - √5) is,
⇒ (2 + √5) (2 - √5) = - 1
We have to given that,
An expression to simplify,
⇒ (2 + √5) (2 - √5)
Now, We can simplify it by using formula,
⇒ (a - b) (a + b) = a² - b²
Hence, We get;
⇒ (2 + √5) (2 - √5)
⇒ (2² - √5²)
⇒ 4 - 5
⇒ - 1
Therefore, The product of expression (2 + √5) (2 - √5) is,
⇒ (2 + √5) (2 - √5) = - 1
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The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations?
(a) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n = 26, t = 2.55, a = 0.01
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n = 26, t = 3.95
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Answer:
Option C - Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
Step-by-step explanation:
We are given;
n = 15
t-value = 1.66
Significance level;α = 0.05
So, DF = n - 1 = 15 - 1 = 14
From the one-sample t - table attached, we can see that the p - value of 0.06 at a t-value of 1.66 and a DF of 14
Now, since the P-value is 0.06,it is greater than the significance level of 0.05. Thus we do not reject the null hypothesis. We conclude that there is not sufficient evidence that the true diameter differs from 0.5 in.
In horse race betting, a trifecta bet is one in which you try to pick which horses will finish first, second, and third, in the correct order. If 8 horses are running in a race and you randomly place a trifecta bet, what is the probability of winning the bet
Answer:
The probability of winning the bet is 1/336
Step-by-step explanation:
We should understand that there is only one possible arrangement of the winning selection
Now, the horse that comes first can be selected in 8 ways given that all the horses have equal chances
The horse that comes second can be selected in 7 ways given that all the horses have equal chances
The horse that comes third can be selected in 6 ways given that all the horses have equal chances
Now the total number of ways of selection would be;
8 * 7 * 6 = 336
Since there is only one of the selections that is correct, the probability of making the correct choice is thus 1/336
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answer
240cm^2 (i think)
Step-by-step explanation:
find the area of each side then add
I got the 90 and 8.9 for them but it’s wrong. I really confused now. What is the right answer??? Can someone explain to me ASAP?!!!!
Answer:
[tex] A = 70.6 [/tex] ≈ 71°
[tex] x = 36.5 [/tex]
Step-by-step explanation:
Step 1: Use the Law of sine to find A
[tex] \frac{sin(A)}{38} = \frac{sin(44)}{28} [/tex]
Cross multiply:
[tex] sin(A)*28 = sin(44)*38 [/tex]
[tex] sin(A)*28 = 0.695*38 [/tex]
Divide both sides by 28:
[tex] \frac{sin(A)*28}{28} = \frac{0.695*38}{28} [/tex]
[tex] sin(A) = 0.9432 [/tex]
[tex] A = sin^{-1}(0.9432) [/tex]
[tex] A = 70.6 [/tex]
A ≈ 71°
Step 2: find the measure of the angle opposite side x
Angle opposite side x = 180 - (71+44) (sum of triangle)
= 180 - 115 = 65°
Step 3: find x using the law of sines
[tex] \frac{x}{sin(65)} = \frac{28}{sin(44)} [/tex]
[tex] \frac{x}{0.906} = \frac{28}{0.695} [/tex]
Multiply both sides by 0.906
[tex] x*0.695= 28*0.906 [/tex]
Divide both sides by 0.695
[tex] \frac{x*0.695}{0.695} = \frac{28*0.906}{0.695} [/tex]
[tex] x = \frac{28*0.906}{0.695} [/tex]
[tex] x = 36.5 [/tex]
Factories fully 18x-9
Answer:
Factor 9 out of 18x.
9(2x)−9
Factor 9 out of −9
9(2x)+9(−1)
Factor 9 out of 9(2x)+9(−1)
9(2x−1)
Answer:
9 ( 2x - 1 )
Step-by-step explanation:
→ Look for the HCF of the whole numbers
HCF of 18 and 9 is 9
→ Put 9 outside the brackets
9 ( ? - ? )
→ Perform the calculation 18x ÷ 9 to determine the first question mark
18x ÷ 9 = 2x ⇔ 9 ( 2x - ? )
→ Perform the calculation 9 ÷ 9 to determine the second question mark
9 ÷ 9 = 1 ⇔ 9 ( 2x - 1 )
What is the 13th term of this arithmetic sequence? 132, 135, 138, 141, …
a 168
b 172
c 176
d 179
Answer:
182
Step-by-step explanation:
The sequence has a common difference of +3.
Answer:
It's none of those. It's supposed to be 171.
Step-by-step explanation:
That's because in an arithmetic sequence it's a list of numbers with a definite pattern, and all you're doing is adding 3 to each number.
Find the area of the polygon shown in the figure.
Answer:
Hey there!
Area for a triangle: 0.5bh, where b is the base, and h is the height.
Plugging in the values: 0.5(4)(8), or simplified to 16.
The area of the polygon is 16 units^2
Hope this helps :)
Answer:
[tex]\boxed{16 \: units^2}[/tex]
Step-by-step explanation:
Apply formula for area of a triangle.
Area of a triangle = [tex]\frac{1}{2} bh[/tex]
[tex]b:base\\h:height[/tex]
The base is 4 units. The height is 8 units.
[tex]\frac{1}{2} (4)(8)[/tex]
[tex]\frac{1}{2} (32)=16[/tex]
An urn contains 3 one-dollar bills, 1 five-dollar bill and 1 ten-dollar bill. A player draws bills one at a time without replacement from the urn until a ten-dollar bill is drawn. Then the game stops. All bills are kept by the player. Determine: (A) The probability of winning $12. (B) The probability of winning all bills in the urn. (C) The probability of the game stopping at the second draw.
Hey there! I'm happy to help!
PART A
There are 3 $1 bills, 1 $5 bill, and 1 $10 bill. This gives us 5 total bills.
First, we want to find the probability of winning $12. Well, to win, you have to draw the $10 bill. You only have room for two dollars beforehand to equal $12 dollars after pulling out the ten. So, this is the probability of drawing two one dollar bills and the the ten. Let's calculate this below.
[tex]\frac{3}{5} *\frac{1}{2} *\frac{1}{3} =\frac{1}{10}[/tex]
Where did I get these numbers from? Well 3 of the 5 bills are $1, so the first probability is 3/5. Then, if we draw one of the $1 bills, there are only 2 of those left and 4 total bills, so the probability is then one half. Finally, there would be only 3 left and you need to pick the $10 bill, which is a probability of 1/3.
The probability of winning $12 is 1/10 or 10%.
PART B
Now, we want to find the probability of picking every single bill before the ten. This means that we pick the three one dollar bills and the five dollar bill before the ten.
To pick the first $1 bill, our probability is 3/5, and then for the second it is 1/2. For the third, there are three total cards and 1 $1 bill, so the probability is 1/3. Then we have a 1/2 chance of picking the $5 bill over the $10 bill, giving us this solution.
[tex]\frac{3}{5} * \frac{1}{2} * \frac {1}{3} * \frac{1}{2}= \frac{1}{20}[/tex]
The probability of winning all bills in the urn is 1/20 or 5%.
PART C
For this event, we want to get any bill that isn't the $10 and then we want the $10 on the second one.
Since there are 4 bills that aren't the $10, our first probability is 4/5. Then, we only have 4 left, with 1 being the $10, so our second probability is 1/4.
[tex]\frac{4}{5}*\frac{1}{4}=\frac{1}{5}[/tex]
The probability of the game stopping at the second draw is 1/5 or 20%.
Have a wonderful day! :D
The probability of winning $12 will be 0.15.
How to calculate probability?The game stops after drawing$10 bill. There can also be 2 draws of $2 and $10 to make $12.
Therefore, the probability of winning $12 will be calculated thus:
= Probability of getting $2 × probability of getting $10
= 3/5 × 1/4
= 0.15
The probability of winning all balls in the urn will be:
= 4/5 × 3/4 × 2/3 × 1/2
= 0.2
Lastly, the probability of the game stopping at the second draw will be:
= First draw × Second draw
= 4/5 × 1/4
= 0.2
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What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
2. Tomás compró una bicicleta en $199.900. Primero, canceló la mitad y el resto en 7 cuotas de igual valor, con un interés total de $4000. ¿Cuánto es el valor de cada cuota?
Answer:
Cada cuota tendrá un valor de $14,850.
Step-by-step explanation:
Dado que Tomás canceló la mitad del valor de la bicicleta, la cual costaba $199.900, el valor pagado al inicio fue de $99,950 (199,900 / 2).
Luego, para el valor restante, Tomás suscribió a una financiación con un interés de $4,000, elevando el monto a pagar a $103,950, pagaderos en 7 cuotas. Por lo tanto, dichas cuotas tendrán cada una un valor de $14,850 (103,950 / 7).
Emma buys 3 and two-thirds yards of blue fabric and some yellow fabric at a store. She buys a total of 5 and one-third yards of fabric. The equation 5 and one-third = 3 and two-thirds + y can be used to represent this situation, where y is the number of yards of yellow fabric she buys. How much yellow fabric does she buy?
Answer:
A) 1 2/3 yards
Step-by-step explanation:
Hope this helped
Answer:
The answer is A
Let me finish the quiz then upload a picture to this answer showing you the correct answer is A
Step-by-step explanation:
Please Help!!! Find X for the triangle shown.
Answer:
[tex] x = 2 [/tex]
Step-by-step explanation:
Given a right-angled triangle as shown above,
Included angle = 60°
Opposite side length = 3
Adjacent side length = x
To find x, we would use the following trigonometric ratio as shown below:
[tex] tan(60) = \frac{3}{x} [/tex]
multiply both sides by x
[tex] x*tan(60) = \frac{3}{x}*x [/tex]
[tex] x*tan(60) = 3 [/tex]
Divide both sides by tan(60)
[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]
[tex] x = \frac{3}{tan(60} [/tex]
[tex] x = 1.73 [/tex]
[tex] x = 2 [/tex] (approximated to whole number)
Simplify the polynomial, then evaluate for x=3 x^2+2x-3-2x^2+x+4
Answer:
The answer is
19Step-by-step explanation:
x² + 2x - 3 - 2x² + x + 4
Group like terms
That's
x² - 2x² + 2x + x - 3 + 4
Simplify
- x² + 3x + 1
when x = 3
We have
(-3)² + 3(3) + 1
9 + 9 + 1
18 + 1
19
Hope this helps you
A circle has a radius of 8ft. Find the length s of the arc intercepted by a central angle of π3 radians. Do not round any intermediate computations, and round your answer to the nearest tenth.
Answer:
8.4ft
Step-by-step explanation:
Formula for calculating the length of an arc is expressed as [tex]L = \frac{\theta}{360} * 2\pi r\\[/tex]
[tex]\theta[/tex] is the central angle = π/3 rad
r is the radius of the circle = 8ft
Substituting the values into the formula above we have;
[tex]L =[/tex] [tex]\frac{(\frac{\pi}{3} )}{2 \pi} * 2\pi (8)\\\\[/tex]
[tex]L = \frac{\pi}{6 \pi} * 2\pi(8) \\\\L = 1/6 * 16\pi\\\\L = 8\pi/3\\\\L = \frac{8(22/7)}{3} \\\\L = \frac{8*22}{7*3}\\ \\L = 176/21\\\\L = 8.4 ft (to\ the\ nearest\ tenth)[/tex]
Hence, the length of the arc s is approximately 8.4 ft.
Use differentials to estimate the amount of material in a closed cylindrical can that is 20 cm high and 8 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.1 cm thick. Note, you are approximating the volume of metal which makes up the can (i.e. melt the can into a blob and measure its volume), not the volume it encloses
Answer:
The volume is [tex]dV = 19.2 \pi \ cm^3[/tex]
Step-by-step explanation:
From the question we are told that
The height is h = 20 cm
The diameter is d = 8 cm
The thickness of both top and bottom is dh = 2 * 0.1 = 0.2 m
The thickness of one the side is dr = 0.1 cm
The radius is mathematically represented as
[tex]r = \frac{d}{2}[/tex]
substituting values
[tex]r = \frac{8}{2}[/tex]
[tex]r = 4 \ cm[/tex]
Generally the volume of a cylinder is mathematically represented as
[tex]V_c = \pi r^2 h[/tex]
Now the partial differentiation with respect to h is
[tex]\frac{\delta V_v}{\delta h} = \pi r^2[/tex]
Now the partial differentiation with respect to r is
[tex]\frac{\delta V_v}{\delta r} = 2 \pi r h[/tex]
Now the Total differential of [tex]V_c[/tex] is mathematically represented as
[tex]dV = \frac{\delta V_c }{\delta h} * dh + \frac{\delta V_c }{\delta r} * dr[/tex]
[tex]dV = \pi *r^2 * dh + 2\pi r h * dr[/tex]
substituting values
[tex]dV = \pi (4)^2 * (0.2) + (2 * \pi (4) * 20) * 0.1[/tex]
[tex]dV = 19.2 \pi \ cm^3[/tex]
(I deleted my answer because it was incorrect)
WILL MARK AS BRAINLIEST 4. Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is: 52C3=52!/49!3! 52C3=22100 Calculate the probability of getting a hand that has exactly two aces in it (A A X). Do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above. Part A: Use the multiplication principle to tell the total number of three-card hands (permutations) that can be made with two aces. (2 points) Part B: In the answer from Part I, each two-ace hand got counted twice. For example, A A X got counted as a separate hand from A A X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?(2 points) Part C: Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. (2 points)
Answer:
Part A- 6
Part B- 3
Part C- 3/22100
Step-by-step explanation:
Part A-
Use the permutation formula and plug in 3 for n and 2 for k.
nPr=n!/(n-k)!
3P2=3!/(3-2)!
Simplify.
3P2=3!/1!
3P2=6
Part B-
Use the combination formula and plug in 3 for n and 2 for k.
nCk=n!/k!(n-k)!
3C2=3!/2!(3-2)!
Simplify.
3C2=3!/2!(1!)
3C2=3
Part C-
It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.
I believe the answer is 3/22100
I honestly suck at probability but I tried my best.
Find the work done by the force field F(x, y) = xi + (y + 5)j in moving an object along an arch of the cycloid r(t) = (t − sin(t))i + (1 − cos(t))j, 0 ≤ t ≤ 2π.
Integrate the force field along the given path (call it C):
[tex]W=\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=\int_0^{2\pi}\mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}\bigg((t-\sin t)\,\mathbf i+(6-\cos t)\,\mathbf j\bigg)\cdot\bigg((1-\cos t)\,\mathbf i+\sin t\,\mathbf j\bigg)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}(t-t\cos t+5\sin t)\,\mathrm dt=\boxed{2\pi^2}[/tex]
By direct calculation we will find that the work done is equal to 2π²
The formula to compute the work done is given by:
[tex]W = \int\limits^a_b {F(x(t), y(t))\cdot\frac{dr(t)}{dt} } \, dt[/tex]
Here we have:
[tex]r(t) = (t - sin(t))i + (1 - cos(t))j[/tex]
This means that:
[tex]x(t) = (t - sin(t))\\y(t) = (1 - cos(t))\\\\\frac{dr(t)}{dt} = (1-cos(t))i + sin(t)j = (1-cos(t), sin(t))[/tex]
And we know that 0 ≤ t ≤ 2π, so b = 0 and a = 2π
Replacing that in the work integral we get:
[tex]W = \int\limits^{2\pi}_0 {(t - sin(t), 1 - cos(t) + 5)\cdot(1-cos(t), sin(t))} \, dt \\\\W = \int\limits^{2\pi}_0 {(t - sin(t), 6 - cos(t))\cdot(1-cos(t), sin(t))} \, dt\\\\W = \int\limits^{2\pi}_0 {(-t*cos(t) +t-sin(t)+ cos(t)*sin(t)+ 6*sin(t) - cos(t)*sin(t) )} \, dt\\\\W = \int\limits^{2\pi}_0 {(-cos(t)*t + 5*sin(t) + t)} \, dt \\\\[/tex]
the sin(t) integral can be removed because it is equal to zero, so we get:
[tex]W = \int\limits^{2\pi}_0 {(-cos(t)*t + t)} \, dtW = [(-t*sin(t) - cos(t)) + \frac{t^2}{2} ]^{2\pi}_0\\\\W = -2\pi*sin(2\pi) - cos(2\pi) + 0*sin(0) + cos(0) + \frac{(2\pi)^2}{2} - \frac{(0)^2}{2}\\\\W = 2\pi^2[/tex]
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You are returning from Mexico and want to convert 5,00 pesos to US dollar . The rate of exchange that day is 1 pesos is 0.55 . How many dollars will you receive for your pesos ?
Hey there! I'm happy to help!
We see that 1 peso is equal to 0.55 U.S. dollars. So, the amount we will get in U.S dollars is the same as $5000×0.55 because 0.55 US dollars is equal to one peso!
5000×0.55=2750
Therefore, you will receive $2750.
Have a wonderful day!
A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x+6y=7.50 10x+5y=8.75
Answer:
x = $0.50
y= $0.75
Step-by-step explanation:
1. Multiply the equations to have the same coefficients
5(6x + 6y = 7.5) → 30x + 30y = 37.5
3(10x + 5y = 8.75) → 30x + 15y = 26.25
2. Subtract the equations
30x + 30y = 37.5
- 30x + 15y = 26.25
15y = 11.25
3. Solve for y by dividing both sides by 15
y = 0.75
4. Plug in 0.75 for y into one of the equations
6x + 6(0.75) = 7.5
5. Simplify
6x + 4.5 = 7.5
6. Solve for x
6x = 3
x = 0.5
Answer:
The cost of one apple is $0.5
The cost of one orange is $0.75
Step-by-step explanation:
Given information
The cost of an apple = [tex]x[/tex]
The cost of an orange = [tex]y[/tex]
Equation to find the values are:
[tex]6x=6y=7.50\\10x+5y=8.75[/tex]
Now, convert the equations to have same coefficient as:
[tex]5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25[/tex]
Now, on solving the above equation by subtracting one from another.
We get,
[tex]15y=11.25\\y=0.75[/tex]
Now , put the value of [tex]y[/tex] in one equation to find the value of [tex]x[/tex].
As,
[tex]6x+4.5=7.5\\x=0.5[/tex]
Hence,
The cost of one apple is $0.5
The cost of one orange is $0.75
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find the product 8x(2x^2+8x-5)
Answer:
16x^3 +64x^2 -40x
Step-by-step explanation:
Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:
8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)
= 16x^3 +64x^2 -40x
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the Algebraic equation by replacing the tens digit with x.
Let a be the number in the 10s place and b in the 1s place. Then the original two-digit number is 10a + b.
The sum of the digits is 5:
a + b = 5
Subtract 9 from the original number, and we get the same number with its digits reversed:
(10a + b) - 9 = 10b + a
Simplifying this equation gives
9a - 9b = 9
or
a - b = 1
Add this to the first equation above:
(a + b) + (a - b) = 5 + 1
2a = 6
a = 3
Then
3 - b = 1
b = 2
So the original number is 32. Just to check, we have 3 + 2 = 5, and 32 - 9 = 23.
A satellite dish is being designed so that it can pick up radio waves coming from space. The satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 50 ft above the ground. Using the ground as the x-axis, where should the base of the satellite be positioned? Which equation best describes the equation of the satellite?
Answer:
[tex]y=\frac{x^2}{100}+2500[/tex]
Step-by-step explanation:
Given that the satellite is in the shape of parabola and will be positioned above the ground such that its focus is 50 ft, above ground.
let the point at the ground be (0,0) and focus (0,50). Thus, The base is at equal distance from the ground and focus that the vertex is at
(h,k) =(0,25).
Obtain the equation that describes the equation of the satellite as,
[tex](x-h)^2 =4a(y-k)\\
\Rightarrow (x-0)^2=4(25)(y-25)\\
\Rightarrow x^2=100(y-25)\\
\Rightarrow x^2 =100y-2500\\
\Rightarrow y=\frac{x^2}{100}+2500[/tex]
Thus, the equation of satellite is [tex]y=\frac{x^2}{100}+2500[/tex]
Answer:
(0, 25); y = one over one hundred x2 + 25
Step-by-step explanation:
If your on question 7 of (04.04 MC)
It should be the third option. (C)
Please answer this correctly without making a mistake I need a correct answer
Answer: 45.5
Step-by-step explanation:
Im in 6th grade and all you had to do was add 18.3 and 27.2 and you’ll get 45.5
Answer:
The garbage dump is 58.3 miles west of the hotel, and the hotel is 57.1 miles west of the hardware store. The hardware store is 44.8 miles west of the library. The hardware store is 57.9 miles north of the office supply store, and the office supply store is 55.5 miles north of the science lab.
Step-by-step explanation:
What is the initial value of the equation shown? y = −7x − 6 −13 −7 −6 −1
Answer:
-6.
Step-by-step explanation:
The equation is y = -7x - 6.
The initial value is found when x = 0.
y = -7(0) - 6
y = 0 - 6
y = -6
Hope this helps!
Rewriting the Equation:
Answer:
7x+y=-33
Step-by-step explanation:
1.) Combine Like Terms: y=-7x-33
2.) Move the variable to the left side and use the inverse operation:
y+7x=-33
3.) Reorder terms using commutative property since x comes before y:
7x+y=-33
If you want to find the function then tell me.
prove identity trigonometric equation
[tex]2 \tan(x) = \frac{ \cos(x) }{ \csc(x - 1) } + \frac{ \cos(x) }{ \csc(x + 1) } [/tex]
Explanation:
The given equation is False, so cannot be proven to be true.
__
Perhaps you want to prove ...
[tex]2\tan{x}=\dfrac{\cos{x}}{\csc{(x)}-1}+\dfrac{\cos{x}}{\csc{(x)}+1}[/tex]
This is one way to show it:
[tex]2\tan{x}=\cos{(x)}\dfrac{(\csc{(x)}+1)+(\csc{(x)}-1)}{(\csc{(x)}-1)(\csc{(x)}+1)}\\\\=\cos{(x)}\dfrac{2\csc{(x)}}{\csc{(x)}^2-1}=2\cos{(x)}\dfrac{\csc{x}}{\cot{(x)}^2}=2\dfrac{\cos{(x)}\sin{(x)}^2}{\cos{(x)}^2\sin{(x)}}\\\\=2\dfrac{\sin{x}}{\cos{x}}\\\\2\tan{x}=2\tan{x}\qquad\text{QED}[/tex]
__
We have used the identities ...
csc = 1/sin
cot = cos/sin
csc^2 -1 = cot^2
tan = sin/cos
Does the data in the table represent a direct variation or an inverse variation write an equation to model the data in the table x 6,8,12,20 y 9,12,18,30
Answer:
direct variation
Step-by-step explanation:
For direct variation k = [tex]\frac{y}{x}[/tex] ← k is the constant of variation
For inverse variation k = yx
Expressing the data as ordered pairs
(6, 9), (8, 12), (12, 18), (20, 30)
k = [tex]\frac{9}{6}[/tex] = [tex]\frac{12}{8}[/tex] = [tex]\frac{18}{12}[/tex] = [tex]\frac{30}{20}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5 ← indicating direct variation
Equation is
y = kx = 1.5x
6th grade math, help me please.
Answer:
1:3
Step-by-step explanation:
3/3=1
9/3=6
Answer:
1 : 3Option A is the correct option.
Step-by-step explanation:
Given,
Number of pears = 3
Number of apples = 9
Find : Ratio of the number of pears to the number of apples on the fruit salad
Now,
[tex] \frac{pear}{apples} [/tex]
Plug the values
[tex] = \frac{3}{9} [/tex]
Divide the numerator and denominator by 3
[tex] = \frac{3 \div 3}{9 \div 3} [/tex]
Divide the numbers
[tex] = \frac{1}{3} [/tex]
It can be written as :
1 : 3
Hope this helps..
Best regards!!!
Write the equation of the line, in point-slope form. Identify (x, y) as the point (-2, 2). Use the box provided or the upload
option to submit all of your calculations and final answers.
Answer:
y = -x + 0
Step-by-step explanation:
well the equation of a line is y = mx + b
m = the slope , b = the y-intercept
m = y2 - y1 / x2 - x1
m = -1
and b is the y-intercept of the line.
finally:
y = -1x + 0