Answer:
[tex]64\ units^{3}[/tex]
Step-by-step explanation:
we have
[tex]V=s^{3}[/tex]
This is the formula to calculate the volume of a cube
where
s is the length side of the cube
In this problem we have
[tex]s=4\ units[/tex]
substitute
[tex]V=4^{3}=64\ units^{3}[/tex]
A philanthropist deposits $2,000 in a trust fund that pays 5.0% interest, compounded continuously. the balance will be given to the college from which the philanthropist graduated after the money has earned interest for 20 years. how much will the college receive? (round your answer to the nearest cent.)
The college will receive an amount of $5436.56.
What is Compound Interest?Compound interest is different from simple interest. In compound Interest, interest amount will vary each year. Interest is calculated first on the principal amount and then interest is the accumulated interest on the previous year.
Compound interest compounded continuously means interest is accumulating not within a month or year, but continuously.
If compound interest is compounded continuously, then the formula for calculating the final amount is,
A = P e^rt
where A is the final amount, P is the principal amount, r is the rate of interest and t is the time period.
Here, P = $2,000
r = 5% = 5/100 = 0.05
t = 20 years
A = 2000 × e^(0.05 × 20)
= 2000 × e^1
= 2000e
The value of e = 2.7182818..
A = 2000 × 2.7182818
= 5436.5636 ≈ 5436.56
Hence by the amount deposited by philanthropist, if the interest is compounded continuously, the college will receive $5436.56.
To learn more about Compound Interest, click :
https://brainly.com/question/14295570
#SPJ5
The lighthouse on the beach casts a shadow that is 4848 feet long. Your friend is 5.55.5 feet tall and casts a shadow that is 2.22.2 feet long. What is the height of the lighthouse?
The equation for line r can be written as y =-1 5 x – 1 .Line s includes the point (10, 4)and is parallel to line r. What is the equation of line s?
the three inside angles (A, B, C) of a right angled triangle are in the ratio 7:18:11. The smallest angle is 35 degrees. Work out the angle A, B,C
The three inside angles (A, B, C) of a right angled triangle are [tex]\rm \angle A = 35^\circ[/tex] which is the smallest angle, [tex]\rm \angle B = 90^\circ[/tex] which is the right angle and [tex]\rm \angle C = 55^\circ[/tex] which is the third angle of the triangle.
Given :
[tex]\rm \angle A :\angle B:\angle C = 7:18:11[/tex]Smallest angle = [tex]35^\circ[/tex]To solve this kind of problems first let x be in degree. So, angle A, angle B and angle C beecomes:
[tex]\rm \angle A = 7x[/tex] ----- (1)
[tex]\rm \angle B = 18x[/tex] ----- (2)
[tex]\rm \angle C = 11x[/tex] ----- (3)
From the properties of triangle, the sum of interior angles of a triangle is [tex]180^\circ[/tex].
[tex]\rm \angle A +\angle B+\angle C = 180^\circ[/tex] --- (4)
Now, put the values of [tex]\rm \angle A,\;\angle B,\;and \; \angle C[/tex] in equation (4).
[tex]7x+18x+11x=180^\circ[/tex]
[tex]36x = 180^\circ[/tex]
[tex]x = 5[/tex]
Now, put the value of x in equation (1), (2) and (3).
[tex]\rm \angle A = 7\times 5 = 35^\circ[/tex]
[tex]\rm \angle B = 18\times5 = 90^\circ[/tex]
[tex]\rm \angle C = 11\times5=55^\circ[/tex]
The three inside angles (A, B, C) of a right angled triangle are [tex]\rm \angle A = 35^\circ[/tex] which is the smallest angle, [tex]\rm \angle B = 90^\circ[/tex] which is the right angle and [tex]\rm \angle C = 55^\circ[/tex] which is the third angle of the triangle.
For more information, refer the link given below
https://brainly.com/question/3430995
The area of the base of a pyramid is 15 cm2.
If the height of the pyramid is 4 cm, what is the volume of the pyramid?
20 cm3 60 cm3 120 cm3 180 cm3
1. Estimate the area of the irregular shape. Explain your method and show your work.
Answer:
The estimated area of figure is 30 square units.
Step-by-step explanation:
We need to find the area of the irregular shape.
Draw a quadrilateral as shown below.
It is a trapezium with bases 5 units and 7 units, and height 5 units.
Area of a trapezoid is
[tex]Area=\frac{a+b}{2}\times h[/tex]
where, a, b are bases and h is height.
Substitute a=5,b=7 and h=5 in the above formula.
[tex]Area=\frac{5+7}{2}\times 5[/tex]
[tex]Area=6\times 5[/tex]
[tex]Area=30[/tex]
Therefore, the estimated area of figure is 30 square units.
A large bag of gumballs contains an equal amount of red, orange, yellow, blue, green, pink, purple, black, teal, and brown gumballs. Lane randomly selects 1 marble from the bag. Which of the following represents the probability of selecting an orange, green, teal, black, or purple gumball?
A. 0.6
B. 0.5
C. 0.7
D. 0.8
A regional soccer tournament has 64 participating teams. In the first round of the tournament, 32 games are played. In each successive round, the number of games played decreases by a factor of 1/2. Find the total number of games played in the regional soccer tournament.
Final answer:
To find the total number of games in a 64-team knockout soccer tournament, we observe that the number of games played in each round is half of the previous round, starting from 32 games in round one. By summing the games from all rounds, we determine that a total of 63 games are played in the tournament.
Explanation:
To calculate the total number of games played in a knockout soccer tournament with 64 teams, we can notice that in each round, half of the teams get eliminated and thus the number of games played is halved. Starting with the first round where 32 games are played, we can sum the total number of games for each subsequent round until we reach the final game.
Here's the pattern of games played per round until the final:
1st Round: 32 games2nd Round: 32 games / 2 = 16 games3rd Round: 16 games / 2 = 8 games4th Round: 8 games / 2 = 4 games5th Round: 4 games / 2 = 2 gamesFinal: 2 games / 2 = 1 gameThe total number of games played in the tournament is the sum of the games played in each round:
32 + 16 + 8 + 4 + 2 + 1 = 63 games
Therefore, the total number of games played in the regional soccer tournament is 63 games.
G(x) = x2 − 7x + 7, find g'(a) and use it to find equations of the tangent lines to the curve y = x2 − 7x + 7 at the points (0, 7) and (6, 1).
To find g'(a), take the derivative of G(x) with respect to x. Substitute x-values into g'(a) to find slope of tangent line. Use slope and point to write equation of tangent line.
Explanation:To find g'(a), we need to take the derivative of G(x) with respect to x. The derivative of G(x) is the slope of the tangent line to the curve at any given point. In this case, G(x) = x^2 - 7x + 7, so g'(a) = 2a - 7.
For the point (0, 7), we substitute x = 0 into g'(a) to find the slope of the tangent line at that point:
g'(a) = 2(0) - 7 = -7Therefore, the equation of the tangent line at (0, 7) is y = -7x + 7.
Similarly, for the point (6, 1), we substitute x = 6 into g'(a) to find the slope of the tangent line at that point:
g'(a) = 2(6) - 7 = 5Therefore, the equation of the tangent line at (6, 1) is y = 5x - 29.
Learn more about Tangent Lines here:https://brainly.com/question/31617205
#SPJ2
A television commercial claims thta 9 out 10 dentists surveyed recommended bliss toothpaste. if 450 of the dentists surveyed recommended bliss, then how many did not recommend it?
Which of the following is being constructed in the image?
Answer:
C) A line perpendicular to a given line through a point not on a line.
Step-by-step explanation:
In the given construction we draw a perpendicular line from a point which is not on line.
Please see the attachment for construction and naming of point.
We are given a line s and point P which is not on line. Through point P we draw an arc on line which cut at two points A and B Now we open an compass and mark an arc through point A. Using same arc we cut the arc A through point B at point C.Now we join PC. Such that PC ⊥ to line sThus, C is correct option. " a line perpendicular to a given line through a point not on a line".
k/2 -6=28
solve for k
Can someone please help me with both of these! Thank youuuu!!! ❤️
Consider the following arithmetic sequence 25,19,13,7... is the common difference 6 or -6 ? Explain
Suppose y varies directly with x. If y = –4 when x = 8, what is the equation of direct variation? Complete the steps to write the equation of direct variation. Start with the equation of direct variation y = kx. Substitute in the given values for x and y to get . Solve for k to get . Write the direct variation equation with the value found for k. The equation is
Answer: y = -(1/2)x
Step-by-step explanation: Direct variation of y with x means that:
y = k*x
where k is a real constant.
We know that when y = -4, the value of x is 8. So we can replace these values in the equation and find the value of k.
-4 = k*8
now we divide by 8 into both sides:
-4/8 = k*8/8 = k
-1/2 = k
So the equation is:
y = -(1/2)x
The equation is k = y/x and the value of k is -1/2
What is the equation and the value of k?The equation that can be used to represent direct proportion is y = kx
Where:
y = independent variable k = constant of proportionalityx = independent variableWhen k is made the subject of the formula, the equation becomes:
k = y/x
k = -4/8 = -1/2
To learn more about direct proportion, please check: https://brainly.com/question/12237076
Which term describes a person's previous pattern of borrowing and repaying?
How many combinations are there to make $2.50 using one dollar bills, quarters, and dimes?
Final answer:
To make $2.50 using one dollar bills, quarters, and dimes, there are 7 different combinations.
Explanation:
To make $2.50 using one dollar bills, quarters, and dimes, we can use the concept of combinations. Let's break it down:
Start with the number of one dollar bills:0 one dollar bills: This gives us 0 dollars.1 one dollar bill: This gives us 1 dollar. We need to make $1.50 more with quarters and dimes.2 one dollar bills: This gives us 2 dollars. We need to make $0.50 more with quarters and dimes.Now let's consider the quarters and dimes:0 quarters and 25 dimes: This gives us $2.50.1 quarter and 20 dimes: This gives us $2.50.2 quarters and 15 dimes: This gives us $2.50.3 quarters and 10 dimes: This gives us $2.50.4 quarters and 5 dimes: This gives us $2.50.So, there are 7 different combinations to make $2.50 using one dollar bills, quarters, and dimes.
Determine the probability of getting a 4 when rolling a fair number cube. If Thelma rolls a fair number cube 600 times, how many times can she expect to get a 4?
Write an equation of the line passing through point P (2,3) that is perpendicular to the time y-4=-2(x+3)
The equation of line which is perpendicular to the given line and has a given point is required.
The equation of the line is [tex]y=\dfrac{1}{2}x+2[/tex].
The given line is
[tex]y-4=-2(x+3)\\\Rightarrow y-4=-2x-6\\\Rightarrow y=-2x-2[/tex]
The slope of the given line is [tex]m_1=-2[/tex]
For a line to be perpendicular we have the condition
[tex]m_1m_2=-1\\\Rightarrow m_2=\dfrac{-1}{-2}\\\Rightarrow m_2=\dfrac{1}{2}[/tex]
The point is [tex]P(2,3)[/tex]
The equation will be
[tex]y=m_2x+c\\\Rightarrow 3=\dfrac{1}{2}\times 2+c\\\Rightarrow c=3-1=2[/tex]
[tex]y=\dfrac{1}{2}x+2[/tex]
Learn more:
https://brainly.com/question/19413318
https://brainly.com/question/11767156
The equation of the line passing through point P(2,3) that is perpendicular to the line y-4=-2(x+3) is y = (1/2)x + 2.
Explanation:To find the equation of the line passing through point P(2,3) that is perpendicular to the line y-4=-2(x+3), we need to find the slope of the perpendicular line first. The given line has a slope of -2. The slope of the perpendicular line will be the negative reciprocal of -2, which is 1/2.
Now that we have the slope, we can use the point-slope form of the equation of a line. The equation is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we have y - 3 = (1/2)(x - 2).
This simplifies to y - 3 = (1/2)x - 1, and further simplifies to y = (1/2)x + 2.
Devin started the work shown to solve for the unknown angle measures. 8x – 1 + 9x – 6 = 180 17x – 7 = 180 17x = 187 What are the measures of angles Q and R?
Answer:
[tex]m<R=87\°[/tex]
[tex]m<Q=93\°[/tex]
Step-by-step explanation:
we have that
[tex]m<R=(8x-1)\°[/tex]
[tex]m<Q=(9x-6)\°[/tex]
[tex]m<R+m<Q=180\°[/tex] ------> by supplementary angles
Substitute the values and solve for x
[tex]8x-1+9x-6=180\°[/tex]
[tex]17x-7=180\°[/tex]
[tex]17x=187\°[/tex]
[tex]x=11\°[/tex]
Find the value of angle R
[tex]m<R=(8*11-1)\°=87\°[/tex]
Find the value of angle Q
[tex]m<Q=(9*11-6)\°=93\°[/tex]
The measure of angle Q and R can be obtained by supplementary angle. The supplementary angle is defined as the addition of two angle is [tex]180^{\circ}[/tex].
The angle Q is [tex]93^{\circ}[/tex] and angle R is [tex]87^{\circ}[/tex].
Given:
The equation for unknown angle is,
[tex]8x -1 + 9x - 6 = 180[/tex]
The supplementary angle is,
[tex]\angle R+\angle Q=180^{\circ}[/tex]
Compare the above equation.
[tex]\angle R=(8x-1)^{\circ}\\\angle Q=(9x-6)^{\circ}[/tex]
Solve the given expression.
[tex]\begin{aligned}8x -1 + 9x -6 &= 180\\ 17x - 7 &= 180 \\17x &= 187 \\x&=11\\\end[/tex]
Calculate the Angle R.
[tex]\angle R=(8\times 11-1)\\\angle R=87^{\circ}[/tex]
Calculate the Angle Q.
[tex]\angle Q=(9\times 11-6)\\\angle Q=93^{\circ}[/tex]
Thus, the angle Q is [tex]93^{\circ}[/tex] and angle R is [tex]87^{\circ}[/tex].
Learn more about supplementary angle is here:
https://brainly.com/question/15613251
in a tank that contains only golden platys, the probability of getting a female fish is 30%. If there are 18 female fishin the tank, how many total fish are in the tank?
Using probability concept in mathematics, the total number of fish in the tank would be 60, this is solved by the equation
[tex]X = (18*100)/30[/tex]Explanation:The student's question involves the concept of probability in mathematics. Given that the probability of finding a female golden platy is 30% and there are 18 female golden platys, we can formulate an equation to find the total number of fish. Let's say the total number of fish in the tank is X. Accordingly, we can write 30/100 * X = 18. Solving this equation would give X = 18 / (30/100), which simplifies to
[tex]X = (18*100)/30 = 60[/tex]golden platys in the tank.
Learn more about probability here:https://brainly.com/question/32117953
#SPJ11
Which of these is a verb?
Europe
Pretty
Cup
Glanced
"The correct answer is ""Glanced.""
To determine which of the given words is a verb, we need to understand the function of each word in a sentence. A verb is a word used to describe an action, state, or occurrence, and it can change form to match the tense, mood, voice, aspect, person, and number of the subject.
Let's analyze each word:
- Europe: This is a proper noun, as it refers to a specific geographical location, the continent of Europe.
- Pretty: This is an adjective, as it describes a noun, modifying it to indicate that something has a pleasing appearance.
- Cup: This is a noun, as it names a thing, which in this case is a container used to hold liquids for drinking.
- Glanced: This is a verb, as it describes an action. ""Glanced"" means to look quickly or briefly at something. It is the past tense of the verb ""glance.""
Therefore, ""Glanced"" is the verb among the options provided."
help please!!!!!
Carlotta is constructing an equilateral triangle. She has already constructed the line segment and arc shown.
What should Carlotta do for her next step?
Place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc.
Use the straightedge to draw a line that passes through point P and intersects the arc.
Use the straightedge to draw a line that passes through point Q and intersects the arc.
Place the point of the compass on point Q and draw an arc that intersects the first arc, using a width for the opening of the compass that is less than 1/2PQ.
The next thing that Carlotta should do for the next step is A. Place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc
An equilateral triangle simply refers to the triangle that has all its sides to be equal. An equilateral triangle also means a triangle where all the angles are 60°.
Since she has already constructed the line segment and arc that's shown in the diagram, then the next thing to do is to place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc.
Read related link on:
https://brainly.com/question/17332594
Find the exact value of the trigonometric function. (if an answer is undefined, enter undefined.) tan(30°)
Final answer:
The exact value of tan(30°) is found using the sine and cosine values of 30°, resulting in tan(30°) being approximately 0.577.
Explanation:
To find the exact value of tan(30°), we look at the relationship between the sides of a 30-60-90 triangle or use the definitions of sine and cosine. The sine of 30° (sin(30°)) is 0.500, and the cosine of 30° (cos(30°)) is 0.866. The tangent is the ratio of sine to cosine, so:
tan(30°) = sin(30°) / cos(30°) = 0.500 / 0.866
When you calculate that ratio, you get tan(30°) = approximately 0.577, which is the exact value for tangent of 30 degrees.
Use the graph to fill in the blank.
F(0)=_
If a is a 3-digit integer and b is a 3-digit integer, is the units digit of the product of a and b greater than 5?
Dylan is 6 years younger than Briana. Briana's age can be represented by x. Write an expression representing Dylan's age.
Answer:
x - 6
Step-by-step explanation:
usatestprep
k-12
Multiply.
3⋅3/5
Enter your answer as an improper fraction, in simplified form, in the box.
Answer:
[tex]1\frac{4}{5}[/tex]
Step-by-step explanation:
3 times 3/5
[tex]3 \cdot \frac{3}{5}[/tex]
To multiply whole number by fraction , then we multiply 3 with the numerator
[tex]\frac{3 \cdot 3}{5}[/tex]
[tex]\frac{9}{5}[/tex]
Now write the fraction in mixed form
when we divide 9 by 5, the quotient is 1 and 4 is the remainder
[tex]\frac{9}{5}[/tex]
[tex]1\frac{4}{5}[/tex]
jeunesse earned $725 dollars by working 5 days in a week. What is the average amount that she earned per day?
In triangle abc, the measure of angle b is 20 more than three times the measure of angle
a. the measure of angle c is 55 more than the measure of angle
a. find the measure of each angle