The volume of the cone, calculated using the given slant length and diameter, is approximately 18.84 cubic units, therefore the correct answer is B. 18.84 cubic units.
Explanation:The subject of this question is the volume of a cone. In order to calculate the volume of a cone, you need to use the formula: V = 1/3πr²h. However, in this case, you are given the slant length and the diameter. First, we need to find the radius (r) and the height (h) of the cone. The radius would be half the diameter, so r = 4/2 = 2. Then, from the given slant length (s) and radius (r), we can find the height by using Pythagoras' theorem: h = sqrt(s² - r²) = sqrt(5² - 2²) = sqrt(21). Now we can substitute r and h into the volume formula: V = 1/3*3.14*2²*sqrt(21) which is approximately 18.84 cubic units. So the answer is option B.18.84 cubic units.
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During an endurance race, part of a car's total distance traveled can be found by multiplying its top
speed (150 km/h) by the number of hours that it takes for the car to finish the race. The other part of
the total distance is the distance it takes for the car to get to top speed, in this case, % of a kilometer.
The car takes 0.01 hours to travel the initial % of a kilometer.
If the car reaches top speed, then drives at top speed for 3.75 hours, how far did the car travel during
the race?
1. Solve the problem above using simple arithmetic.
Answer:
563.25 km
Step-by-step explanation:
let [tex]d_1[/tex] be the the distance it takes for the car to get to top speed and [tex]d_2[/tex] be distance traveled can be found by multiplying its top speed (150 km/h) by the number of hours that it takes for the car to finish the race. The total distance d is given as:
[tex]d=d_1+d_2[/tex]
To get [tex]d_1[/tex], the car is initially at rest (i.e 0 km/h) and then it accelerates to a speed of 150 km/hr within 0.01 hrs. Let u = initial velocity = 0 km/hr, v = final velocity = 150 km/hr and the time taken ([tex]t_1[/tex]) = 0.01 hrs. Therefore:
[tex]d_1=(\frac{v+u}{2} )t=(\frac{0+150}{2} )0.01=0.75km[/tex]
To get [tex]d_2[/tex] , we use the formula [tex]d_2[/tex] = v[tex]t_2[/tex], where v =150 km / hr and [tex]t_2[/tex] = 3.75 hrs. Therefore:
[tex]d_2=150*3.75=562.5km[/tex]
[tex]d=d_1+d_2=562.5+0.75=563.25km[/tex]
1. Expand to write an equivalent expression: +(-8.+ 12y)
Answer:
-8 +12y
Step-by-step explanation:
a positive times a negative is negative so it stays the same
Which dimensions cannot create a triangle? Three sides measuring 6 cm, 8 cm, and 10 cm three angles measuring 10 degrees, 25 degrees, and 145 degrees three sides measuring 9 m, 15 m, and 9 m three angles measuring 40 degrees, 70 degrees, and 65 degrees
Answer:
c
Step-by-step explanation:
its correct no neef for an explanation
What is the volume of the following rectangular prism?
Answer:
33 units
Step-by-step explanation:
volume =area of base x height
volume = 9x (3 2/3)
volume= 33
According to given question, The volume of the rectangular prism is 72 cubic units.
The volume of a rectangular prism can be calculated by multiplying the length, width, and height of the prism. Let's say the length of the prism is 6 units, the width is 4 units, and the height is 3 units.
To find the volume, we use the formula: V = length × width × height. Substituting the given values, we get: V = 6 units × 4 units × 3 units. Multiplying the values, we find: V = 72 cubic units. Therefore, the volume of the rectangular prism is 72 cubic units.
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In the figure below, AB is a diameter of circle P.
What is the arc measure of AC on circle P in degrees?
14
C
Answer:
The arc measure of ABC is 221°
Answer:
139 degrees
Step-by-step explanation:
Subtract 41 from 180. You will get 139 degrees. Arc AC is 139 degrees.
-Briannah-
Which situations can be simulated using this spinner? Select three options.
A spinner with 6 equal sections.
A: Predicting the gender of a randomly chosen art teacher if 1 of 3 art teachers is female
B: Predicting the gender of a randomly chosen history teacher if 12 of 15 history teachers are female
C: Predicting the gender of a randomly chosen biology teacher if 8 of 12 biology teachers are female
D: Predicting the gender of a randomly chosen chemistry teacher if 4 of 9 chemistry teachers are female
E: Predicting the gender of a randomly chosen health teacher if 2 of 4 health teachers are female
Answer:
A: Predicting the gender of a randomly chosen art teacher if 1 of 3 art teachers is female.C: Predicting the gender of a randomly chosen biology teacher if 8 of 12 biology teachers are female.E: Predicting the gender of a randomly chosen health teacher if 2 of 4 health teachers are female.Step-by-step explanation:
Notice that the spinner has 6 equal sections.
So, all situations that can be simulated with such spinner must be multiples, divisors of 6, or a number least than 6, that way, we could use the 6 equal-section spinner.
Option A uses 1 of 3, Option B uses 8 of 12, and Option E uses 2 of 4.
Therefore, the anwers are A, C and E.
Answer: A C E
Step-by-step explanation:
The radius of a circle is 8 miles. What is the length of a 90° arc?
Answer:
12.56 miles
Step-by-step explanation:
[tex]l = \frac{ \theta}{360 \degree} \times 2\pi \: r \\ \\ = \frac{ 90 \degree}{360 \degree} \times 2 \times 3.14 \times 8 \\ \\ = \frac{ 1}{4} \times 16 \times 3.14 \\ \\ = 4 \times 3.14 \\ = 12.56 \: miles[/tex]
Hence, length of arc = 12.56 miles
sally invests 10,500 in an account that earns 6% annual simple interest. assuming she makes no additional deposits or withdraws, how much interest will sally earn after 4 years?
Answer:
The interest is: $2520.00
Step-by-step explanation:
P is the principal amount, $10500.00.
r is the interest rate, 6% per year, or in decimal form, 6/100=0.06.
t is the time involved, 4....year(s) time periods.
So, t is 4....year time periods.
To find the simple interest, we multiply 10500 × 0.06 × 4 to get that
A researcher selects two samples of equal size and computes a mean difference of 1.0 between the two sample means. If the pooled sample variance is 4.0, then what is the effect size using the estimated Cohen’s d formula?
Answer:
The Cohen's D is given by this formula:
[tex] D = \frac{\bar X_A -\bar X_B}{s_p}[/tex]
Where [tex] s_p[/tex] represent the deviation pooled and we know from the problem that:
[tex] s^2_p = 4[/tex] represent the pooled variance
So then the pooled deviation would be:
[tex] s_p = \sqrt{4}= 2[/tex]
And the difference of the two samples is [tex] \bar X_a -\bar X_b = 1[/tex], and replacing we got:
[tex] D = \frac{1}{2}= 0.5[/tex]
And since the value for D obtained is 0.5 we can consider this as a medium effect.
Step-by-step explanation:
Previous concepts
Cohen’s D is a an statistical measure in order to analyze effect size for a given condition compared to other. For example can be used if we can check if one method A has a better effect than another method B in a specific situation.
Solution to the problem
The Cohen's D is given by this formula:
[tex] D = \frac{\bar X_A -\bar X_B}{s_p}[/tex]
Where [tex] s_p[/tex] represent the deviation pooled and we know from the problem that:
[tex] s^2_p = 4[/tex] represent the pooled variance
So then the pooled deviation would be:
[tex] s_p = \sqrt{4}= 2[/tex]
And the difference of the two samples is [tex] \bar X_a -\bar X_b = 1[/tex], and replacing we got:
[tex] D = \frac{1}{2}= 0.5[/tex]
And since the value for D obtained is 0.5 we can consider this as a medium effect.
Jasmine invests $2,658 in a retirement account with a fixed annual interest rate of 9% compounded continuously. What will the account be after 15 years
Answer:
$10,253.04
Step-by-step explanation:
You are going to want to use the continuous compound interest formula, which is shown below.
[tex]A = Pe^{rt}[/tex]
P = principal amount
r = interest rate (decimal)
t = time (years)
First, change 9% into a decimal:
9% -> [tex]\frac{9}{100}[/tex] -> 0.09
Next, plug the values into the equation:
[tex]A=2,658e^{0.09(15)}[/tex]
[tex]A=10,253.04[/tex]
The account will have $10,253.04
A wheel with a diameter of 25 in. is in a puddle of water 8.1 in. deep. What is the width of the wheel, AB, at the surface of the water?
Please actually answer the question <3
Answer:
The length AB is 23.4in
Step-by-step explanation:
N/B please see the attached detailed diagram for your reference and better understanding
This problem bothers on the mensuration of flat shapes.
The width AB is the chord of the wheel
The radius of the whee r= 25/2= 12.5in
The depth of the wheel in the puddle is 8.1in
Let b be the distance from the surface AB to the diameter
b= 12.5-8.1 = 4.4in
Applying the formula
Chord Length = 2 *√(r²-b²)
=2*√(12.5²-4.4²)
= 2*√(156.25-19.36)
=2*√(136.89
=2*11.7
=23.4in
any one have the rest of the Surface Area and Volume Unit Test ??? please !!
Answer:
Second option is the right choice.
Step-by-step explanation:
[tex]Volume=2\pi rh+2\pi r^2\\\\V=2\left(3.14\right)\left(13\right)\left(14\right)+2\left(3.14\right)\left(13\right)^2\\\\\approx2205\:in^2[/tex]
Which must be true in order for the relationship ^zyx~^wvu to be correct
Answer:
Correct option: fourth one: ∠Z = ∠W and ∠X = ∠U
Step-by-step explanation:
There are 3 cases that gives similarity of two triangles:
Side-Angle-Side: They should have 2 sides and 1 angle in common
Side-Side-Side: They should have all 3 sides in commom
Angle-Angle: They should have 2 angles in common (therefore the third angle will also be equal)
In the first option, we have a pair of sides being parallel. That is not enough to prove similarity.
In the second option, two angles of the same triangle are equal, that's not enough, because the angles between each triangle can be different.
In the third option, two side of the same triangle are equal, that's not enough.
In the fourth option, two angles of the triangles are equal to each other, so this is the third case mencioned above, therefore it proves the similarity.
Correct option: fourth one.
Similar triangles may or may not be congruent.
The relationship that must be true for [tex]\mathbf{\triangle ZYZ \sim \triangle WVU}[/tex] is (d) [tex]\mathbf{\angle Z \cong \angle W }[/tex] and [tex]\mathbf{\angle X \cong \angle U }[/tex]
From the question, we understand that: [tex]\mathbf{\triangle ZYZ \sim \triangle WVU}[/tex]
The above means that, both triangles are similar (but not congruent). This means that:
The corresponding side lengths cannot be equalThe corresponding angles must be equalIn other words
[tex]\mathbf{\angle Z \cong \angle W }[/tex], [tex]\mathbf{\angle X \cong \angle U }[/tex] and [tex]\mathbf{\angle Y \cong \angle V }[/tex]
Hence, the true relationship is (d) [tex]\mathbf{\angle Z \cong \angle W }[/tex] and [tex]\mathbf{\angle X \cong \angle U }[/tex]
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What should be done to solve the following equation?
c - 7 = 0
Add 7.
Subtract 0 from both sides.
Add 7 to both sides.
Subtract 7 from both sides.
Answer:
Add 7 to both sides
Step-by-step explanation:
c - 7 + 7 = 0 + 7
c = 7
Answer: subtract 5 b
can u pls help i have a few mins left
What is the common denominator of 1/a + 1/b in the complex fraction 1/a-1/b divided by 1/a+ 1/b?
Answer:
common denominator of 1/a + 1/b is ab
however simplifying the complex fraction gives: (b-a)/(b +a)
Step-by-step explanation:
common denominator of 1/a + 1/b
should be the product of the denominators
a*b
so 1/a + 1/b = (b + a)/ab
ao
( 1/a - 1/b) divided by (1/a + 1/b) = (b - a)/(ab) divided by (b+a)/ab
To find the common denominator for 1/a and 1/b within a complex fraction, we use ab. The complex fraction (1/a - 1/b) divided by (1/a + 1/b) can be simplified by multiplying the numerator and denominator by ab, leading to a simplified form of (b² - a²) / (a² + b²).
When finding the common denominator for complex fractions like 1/a and 1/b, it's similar to dealing with real numbers. Given the complex fraction (1/a - 1/b) divided by (1/a + 1/b), we can identify a and b as the denominators. To combine the fractions within the complex fraction, we need a common denominator, which is ab. Thus, the fractions would become (b/a - a/b) and (a/b + b/a), both with a common denominator of ab.
In the complex fraction ((1/a - 1/b) / (1/a + 1/b)), by finding the common denominator, we then rewrite the equation as (b/a - a/b) / (a/b + b/a), which simplifies to (b² - a²) / (a² + b²) when multiplied by ab in both the numerator and the denominator. This process of finding the common denominator allows us to combine and simplify the complex fraction.
Please help last question and I don’t understand
Answer: 282.74
Step-by-step explanation:
V= pi r^2 h = pi * 3^2 * 10 = 282.74
Kayla says that the point labeled C in the diagram below is the center, Raymond says that point C is the radius.
Who is correct and why?
Kayla is correct; the center is a fixed point in the middle of the sphere.
Kayla is correct; the center is a line segment from the center to the surface of the sphere.
Raymond is correct, the radius is the fixed point in the middle of the sphere.
Raymond is correct; the radius is a chord that is from the center to the surface of the sphere.
Answer:
The answers D
Step-by-step explanation:
Answer:
its: A
Step-by-step explanation:
The point which is the center or the middle point is located at the middle of the circle.
Omar filled his gas tank for times last week. Here are the amounts of gas he bought 1.2,13.7,5.04,14. What is the total amount of gas omar bought last week
Answer: 33.94
Step-by-step explanation:
Last week, Omar filled his gas four times. The amounts of gas he bought are 1.2, 13.7, 5.04 and 14.
To get the total amount of gases bought by Omar, we add all the gases her bought the four times together. This gives:
1.2 + 13.7 + 5.04 + 14 = 33.94
This means that Omar bought a total gas of 33.94 last week.
Answer:
The total amount of gas Omar bought last week is 33.94
Step-by-step explanation:
Omar filled his gas four times and the amont of gas he bought are 1.2, 13.7, 5.04 and 14.
to estimate the total amount of gases Omar bought, we will sum up the amount of gas bought
1.2 + 13.7 + 5.04 + 14
= 33.94
Hence, the total amount of gas Omar bought last week is 33.94
If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2 + 96t. Find the maximum height of the projectile.
Answer:
144 feet
Step-by-step explanation:
The quadratic equation is:
[tex]h(t)=-16t^2+96t[/tex]
The general form of a quadratic is [tex]ax^2+bx+c[/tex]
So, we can match the equations and say:
a = -16
b = 96
c = 0
Now, for quadratic equations, the max value occurs at [tex]x=-\frac{b}{2a}[/tex] and the max value is what we get when we put that number in the function. First, lets find the value on which is occurs:
[tex]x=-\frac{b}{2a}\\x=-\frac{96}{2(-16)}\\x=3[/tex]
Now, put x = 3 into the equation:
[tex]h(t)=-16t^2+96t\\h(3)=-16(3)^2+96(3)\\h(3)=144[/tex]
The max height of projectile is 144 feet
Eric is twice as tall as his little brother Kevin. Kevin is also three feet shorter than Eric. If we let E=Eric's height and let K= Kevin's height, translate these two sentences into 2 equations.
Answer:
The 2 equations are E = 2K and K = E-3
Step-by-step explanation:
Let the height of Eric be E
Let the height of Kevin be K
Eric is twice as tall as his little brother Kevin
E = 2K
Kevin is also three feet shorter than Eric
K = E-3
The 2 equations are E = 2K and K = E-3
Final answer:
Eric's height (E) is twice Kevin's height (K), represented by the equation E = 2K. Kevin is three feet shorter than Eric, which gives us the second equation K = E - 3. These equations help us determine their exact heights when solved together.
Explanation:
To translate the given information about Eric and Kevin's heights into two equations, we need to use the given relationship between their heights. From the statement 'Eric is twice as tall as his little brother Kevin,' we can write the first equation as E = 2K. This equation shows that Eric's height (E) is twice Kevin's height (K). The second statement 'Kevin is also three feet shorter than Eric' gives us the equation K = E - 3, which represents that Kevin's height is three feet less than Eric's height.
Together, these two equations can be used to solve for the exact heights of Eric and Kevin.
i’m really confused someone help please
Find the perimeter of the shape given length = x^2+4 and the width = 3x-4.Explain how you found your answer to problem .
Answer:
[tex]2x^{2}+6x[/tex]
Step-by-step explanation:
Perimeter is the distance all round a figure. Given length and width only, then this shale is likely to be a triangle. For a triangle, the area is given by
P=2(l+w)
Where l is the length and w is width.
Substituting w with 3x-4 and l with [tex]x^{2}+4[/tex]
then
[tex]P=2( x^{2}+4 +3x-4)=2( x^{2}+3x)=2x^{2}+6x[/tex]
Therefore, perimeter is [tex]2x^{2}+6x[/tex]
How can you rewrite log798 using the product
property?
Answer:
3 ways!
Step-by-step explanation:
-log72+log749 -log749= (2)-log798=2.356Answer:
log72+log749
log749=2
log798=2.356
Step-by-step explanation:
correct answers on edgn
Kristin drinks 0.5 liters of orange juice with breakfast each day for 15 days. How many milliliters of orange juice does Kristin drink during the 15 days?
Answer:
she drank 7500 milliliters of juice
Step-by-step explanation:
In this question, we are asked to calculate the amount of juice in milliliters consumed by Kristin.
From the question, she drank 0.5 liters per day for 15 days. This means that the total amount she drank for the 15 days will be 0.5 * 15 = 7.5 liters
what we now need to do is to calculate the equivalent of this in milliliters.
To get this, we need to multiply the volume in liters by 1000. This is simply because 1000 milliliters make 1 liter
so that will be 7.5 * 1000 = 7500 milliliters of juice
Final answer:
To find out how much orange juice Kristin drinks over 15 days, convert her daily intake from liters to milliliters and multiply by the number of days. She drinks 7500 milliliters in total.
Explanation:
The question asks how many milliliters of orange juice Kristin drinks during 15 days if she drinks 0.5 liters each day. First, we need to convert liters to milliliters, knowing that 1 liter equals 1000 milliliters. Then, we multiply the daily amount of orange juice by the number of days.
Convert liters to milliliters: 0.5 liters = 500 milliliters (since 0.5 × 1000 = 500).
Multiply by the number of days: 500 milliliters/day × 15 days = 7500 milliliters.
Therefore, Kristin drinks 7500 milliliters of orange juice over 15 days.
Write a rational function f(x) such that f has vertical asymptotes at x = 3 and x = -1, no horizontal asymptote, and end behavior that can be modeled by y = 2x.
Answer:
[tex]f(x)=\frac{2x^3-4x^2-6x}{x^2-2x-3}[/tex]
Step-by-step explanation:
Roots of a denominator in a rational function gives to us the vertical asymptotes. Hence we can take the denominator as
[tex](x-3)(x+1)=x^2-2x-3[/tex]
if we want that the end behavior as y=2x we can choose a polynomial whose factors cancel out with the denominator. Thus
[tex]2x(x-3)(x+1)=2x^3-4x^2-6x[/tex]
Hence, the function is
[tex]f(x)=\frac{2x^3-4x^2-6x}{x^2-2x-3}[/tex]
Hope this helps!!
Which equation could be used to find the length of the hypotenuse?
Triangle A B C. Side A C is 2 feet and side C B is 5 feet. Hypotenuse A B is labeled c.
2 squared + 5 squared = c squared
2 squared + c squared = 5 squared
c squared minus 2 squared = 5 squared
5 squared minus 2 squared = c squared
Answer:
Step-by-step explanation:
leg1² + leg2² = hypotenuse²
AC² + BC² = AB²
2² + 5² = c²
Answer:
2² + 5² = c²
Step-by-step explanation:
2² + 5² = c²
:3
Shota invests $2000 in a certificate of deposit that earns 2% in interest each year.Write a function that gives the total v(t) in dollars of the investment t years from now
Answer:
The correct answer is v(t) = (principal × time × 0.02) if calculated simply and v(t) = Principal × [tex]( 1.02) ^ {time}[/tex] where v(t) is the interest after t years .
Step-by-step explanation:
Principal amount invested by Shota is $2000.
Interest is earned at 2% per year.
Time for which the principal is invested is t years.
Therefore let the total interest be v(t) dollars in t years.
Case 1: Simple Interest.
v(t) = (principal × time × [tex]\frac{r}{100}[/tex] ) = (2000 × t × 0.02) = 40t
Case 2: Compound Interest.
v(t) = Principal × [tex]( 1+ \frac{r}{100}) ^ {t}[/tex] - Principal = 2000 × [tex]( 1.02) ^ {t}[/tex] - 2000.
Marshall's office had already recycled 2 kilograms this year before starting the new recycling plan, and the new plan will have the office recycling 4 kilograms of paper each week. Write an equation that shows the relationship between the weeks w and the paper recycled p.
Write your answer as an equation with p first, followed by an equals sign.
Answer: w x 4 + 2 = p
Step-by-step explanation:
W = Week
P = Paper
4 kg a week would be 4 x w
you also must add the 2 kilograms at the start of the year
How many solutions does the graph of x2 + 100 = 0 have?
Answer:
there are two solutions
Step-by-step explanation:
x=10
x=-10