Answer:
Because this is simple interest, the money will earn the same amount of money each year: 4% of $2500.
0.04×2500=100
4% of 2500 is 100, so...
$200÷$100 Per Year= 2Years
Answer:
It will take 2 months let me know if I'm wrong
Step-by-step explanation:
Which of the following shapes is described as having one triangular base and three lateral faces?
square pyramid
triangular prism
triangular pyramid
cone
NEXT QUESTION
ASK FOR HELP
Answer: triangular pyramid
Step-by-step explanation:
Answer:
Triangular Pyramid
Step-by-step explanation:
A triangular pyramid consists of 1 triangular base, with three lateral faces also in the shape of a triangle. Its net consists of 4 triangles, and is a solid 3-Dimensional figure. I hoped this helped.
How many 5-letter “words” can be formed from the letters of the word FORMULATED, if each will have the vowels at the two ends on the “word”?
Final answer:
To calculate the number of 5-letter "words" with vowels on the ends from 'FORMULATED', you multiply the number of ways to choose the two vowels (4 x 3) by the number of ways to choose the three different consonants (6P3; 6 x 5 x 4), resulting in 1440 different possible "words."
Explanation:
To determine the number of 5-letter "words" that can be formed from the letters of the word FORMULATED with vowels at both ends, we need to consider two parts: the selection of vowels and the selection of consonants. The word FORMULATED contains four vowels (O, U, A, E) and six consonants (F, R, M, L, T, D).
First, we choose the vowels for the ends. There are 4 vowels, which means we can select the first vowel in 4 ways. After selecting the first vowel, we can still choose the second vowel from the remaining 3 vowels (since we are allowing repetitions). This gives us 4 x 3 possibilities for the vowels.
Now we select the consonants for the center three positions. We have 6 different consonants to choose from, and since each position must be filled with a unique letter, we can select these in 6P3 (6 permute 3) ways, which is calculated as 6 x 5 x 4.
Finally, to find the total number of 5-letter "words," we multiply the number of ways to choose the vowels by the number of ways to choose the consonants, giving us 4 x 3 x 6 x 5 x 4 which equals 1440 possible "words."
Write the expression in complete factored form.
x2 – 3x + xy - 3y
NEED HELP WITH TRIG please show work as i am trying to learn the material i'm really puzzled. its soh cah toa but i don't remember how to do it
Answer:
see below
Step-by-step explanation:
5. sin 31 = opp/ hyp
sin 31 = 34 /x
x = 34 / sin 31
x =66.0145369
tan 31 = opp /adj
tan 31 = 34/y
y = 34/ tan 31
y= 56.5855024
6. Pythagorean theorem to find z
9^2+12^2 = z^2
81+144 = z^2
225 = z^2
z =sqrt(225) =15
sin x = opp / hyp
sin x = 9/15
take the inverse sin
x = sin^ -1 (9/15) = 36.86989765
sin y = opp / hyp
sin y = 12/15
take the inverse sin
y = sin^ -1 (12/15) = 53.13010235
Answer:
1. sin(31) = opposite/hypotenuse
sin(31) = 34/x
x = 34/sin(31) = 66.0145369
x = 66.0°
tan(31) = opposite/adjacent
tan(31) = 34/y
y = 34/tan(31) = 56.5855024
y = 56.6°
2. tan(x) = opposite/adjacent
tan(x) = 9/12
x = 36.86989765
x = 36.9°
y = 180 - 90 - x
y = 53.13010235
y = 53.1°
z² = 9² + 12²
z² = 225
z = 15
If Logan's family can drive 23 1/8 miles on 1 gallon of gas, how far can they drive on 17 gallons?
Answer:
393 1/8 miles
Step-by-step explanation:
Distance driven in 1 gallon of gas = 23 1/8 miles
23 1/8 miles is mixed fraction.
converting 23 1/8 into improper fraction
23 1/8 = (23*8 + 1)/8 = 185/8
Thus 1 gallon of gas can drive 185/8 miles. ____________1
Since distance for 17 gallons is needed.
we multiply both gallon of gas and distance with 17.
1 *17 gallon of gas can drive 185/8*17 miles
17 gallon of gas can drive (185/8)*17 miles
=>17 gallon of gas can drive (3,145)/8 miles
converting (3,145)/8 miles into mixed fraction we have 393 1/8 .
Thus, Logan's family can drive 393 1/8 miles on 17 gallons.
The school band is selling sweatshirts and baseball caps to raise $2000 to attend a band competition. Sweatshirts cost $25 each and baseball caps cost $10 each. The equation 25x + 10y = 2000 models this situation, where x is the number of sweatshirts sold and y is the number of basebal caps sold.
Answer:
X-intercepts: (80,0)
y-intercepts: (0,200)
Step-by-step explanation:
(To find the x-intercept, substitut in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y. As shown in the pictur)
The x-intercept and y-intercept of the equation will be (8, 0) and (0, 20).
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The school band is selling sweatshirts and baseball caps to raise $2000 to attend a band competition.
Sweatshirts cost $25 each and baseball caps cost $10 each.
The equation 25x + 10y = 2000 models this situation.
Where x is the number of sweatshirts sold and y is the number of baseball caps sold.
Then the x-intercept will be
25x = 200
x = 8
The x-intercept will be (8, 0).
And the y-intercept will be
10y = 200
y = 20
The y-intercept will be (0, 20).
The x-intercept and y-intercept of the equation will be (8, 0) and (0, 20).
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Compute.
53÷ (−12 × −4)
Step-by-step explanation:
53 ÷ (-12 x - 4)
53 ÷ 48
= 1.10416
Last year Boris paid £256 for his car insurance. This year he had to pay £894 for his car insurance work out the percentage increase in the cost of his car insurance.
If you can answer this ASAP it would be really appreciated.
Answer:
349.2%
Step-by-step explanation:
£256 = 100%
£2.56 = 1%
£894 = 349.2%
HELP
Which function is equivalent to y = 3(x + 2)2 + 7?
A y = 3x2 + 12x + 33
B y = 3x2 + 12x + 19
C y = 3x2 + 19
D y = 3x² + 33
Answer:
B y = 3x^2 + 12x + 19
Step-by-step explanation:
y = 3(x + 2)^2 + 7
To expand the square of the binomial,
either recall that (a + b)^2 = a^2 + 2ab + b^2, or use FOIL.
y = 3(x^2 + 4x + 4) + 7
y = 3x^2 + 12x + 12 + 7
y = 3x^2 + 12x + 19
Answer: B y = 3x^2 + 12x + 19
Final answer:
After expanding and simplifying the given function, we find that the equivalent function is y = 3x^2 + 12x + 19, which corresponds to option B.
Explanation:
The task is to find the equivalent function to y = 3(x + 2)2 + 7. We'll start by expanding the square and then distributing the 3 across the resultant terms.
First, expand the square: (x + 2)2 = x2 + 4x + 4.
Next, distribute the 3: 3(x2 + 4x + 4) = 3x2 + 12x + 12.
Finally, add the 7 to complete the expansion: 3x2 + 12x + 12 + 7 = 3x2 + 12x + 19.
Therefore, the equivalent function is B y = 3x2 + 12x + 19.
what are two whole numbers that the square root number 19 falls between
Given points -6,-3 and 8,0 find the slope
Answer:
3/14
Step-by-step explanation:
gradient = (0-(-3))/(8-(-6)) = 3/14
find the area of the triangle whose vertices are x(3,2) y(-1,0)and z(1,-12)
Answer:
The triangle whose vertices are x(3,2) y(-1,0)and z(1,-12).
=> xy = sqrt(4^2 + 2^2) = 4.472
=> xz = sqrt(2^2 + 14^2) = 14.142
=> yz = sqrt(2^2 + 12^2) = 12.166
=> Perimeter/2 = P = (xy + yz + xz)/2 = (4.472 + 14.142 + 12.166)/2 = 15.39
=> Applying Heron's formula, the area of triangle would be:
A = sqrt(P*(P-xy)*(P-xz)*(P-yz))
= sqrt(15.39*(15.39 - 4.472)*(15.39 - 14.142 )*(15.39 - 12.166))
= 26.001
= ~26
Hope this helps!
:)
0.193 ? 0.65
A. <
B. =
C. >
Answer:
A
Step-by-step explanation:
The answer is A, reason why is because if you add a 0 to the end of the number 0.65, the problem would then say; 0.193 < 0.650. So, if you take off the 0. on the front of both decimals it would then say 193 < 650 and 650 is greater than 193.
PLEASE HELP!!!!!!!!!!!!!!!!!! WILL MARK BRAINLIEST IF CORRECT ANSWER!!!!!!!!!!!!!!!!!!1
Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and height of 13 inches?
Part A
Could the baton lie flat on a diagonal along the base of the box?
A. Yes, because the diagonal is 48 inches long.
B. Yes, because the diagonal is 41.4 inches long.
C. No, because the diagonal is 37.3 inches long.
D. No, because the diagonal is 18.4 inches long.
I think C. but need help, is it right? How so?
Part B
Could the baton fit along the interior diagonal of the box? Explain.
Answer:
C.; Yes
Step-by-step explanation:
A)
The longest thing that can fit along the base of the box is sqrt ( 13^2 + 35^2) = 37.3, which is less than 38, so NO, the baton can't lay flat on a diagonal along the base of the box C. No, because the diagonal is 37.3 inches long.
B) The interior diagonal of the box is sqrt(13^2 + 13^2 + 35^2) = sqrt (1563), which is 39.5, which is greater than 38, so YES, the baton can fit along the interior diagonal of the box.
Shannon bought 5 pounds of apples. Bill bought 2 pounds of apples. Which most
closely estimates how many more pounds of apples Shannon bought than Bill?
Answer:
Shannon bought 3 more pounds of apples.
Step-by-step explanation:
5 - 2 is 3.
Answer:
3
Step-by-step explanation:
5-2=3
A regular hexagon is rotated about its center. Which degree measure will carry the regular hexagon onto itself ?
Final answer:
A regular hexagon will coincide with itself when rotated by angles of 60 degrees, or multiples of it like 120, 180, 240, 300, and 360 degrees, because these are the angles of rotational symmetry for a hexagon.
Explanation:
A regular hexagon has six sides of equal length and interior angles that are also equal. When a regular hexagon is rotated about its center, there are specific degree measures for which it will fit exactly onto itself, known as the angles of rotational symmetry. Since a full rotation measures 360 degrees and a hexagon has six sides, we can divide 360 degrees by the number of sides to find the smallest angle of rotation that will carry the regular hexagon onto itself.
The calculation is 360 ÷ 6 = 60 degrees. Therefore, a regular hexagon will coincide with itself every 60-degree turn. Other angles that will carry the hexagon onto itself are multiples of 60 degrees: 120 degrees, 180 degrees, 240 degrees, 300 degrees, and 360 degrees (a full rotation).
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width. Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Write the equation that represents the volume of the storage container in terms of its width. A. V = 6w2 - 12w B. V = 6w2 + 12 C. V = 6w2 - 12 D. V = 6w2 + 12w
The answer is B.) V = 6w2 + 12w
Answer:
V = 6w² + 12w
Step-by-step explanation:
Need help with this ASAP. Anything is appreciated:))
So they seem to intersect around the 35 year mark, and tree B was planted at year 0, so therefore they intersected 35 years after Tree B was planted.
The x coordinate is years since B is planted. Looks like the x coordinate of the intersection is about 35 years.
Answer: 35 years
What is the volume of the rectangular prism?
Answer:
[tex]V= \frac{15}{4}[/tex]
Step-by-step explanation:
To find find the volume of a rectangular prism you need to formula.
V = whl w is the width, h is the height, and l is the length.
It shows that the length of one box is 1/2 cm
To find the width, multiply 1/2 by 2 because there's 2 boxes
To find the height, multiply 1/2 by 3 because there's 3 boxes going up
To find the length, multiply 1/2 by 5 because there's 5 boxes going across
Now that you have the width, height, and length put them into the formula.
[tex]V = (1)(\frac{3}{2})(\frac{5}{2})[/tex] multiply everything together
[tex]V= \frac{15}{4}[/tex]
The volume of the rectangular prism is 15/4.
What is prism?In three dimensional space prism is a polyhedron where two ends are similar.
Given we have the length of one box is 1/2cm.
To find find the volume of a rectangular prism;
volume of rectangular prism = width x height x length.
To find the width,
multiply 1/2 by 2 because there's 2 boxes.
To find the height,
multiply 1/2 by 3 because there's 3 boxes in one column.
To find the length,
multiply 1/2 by 5 because there's 5 boxes in one row.
Now,
volume of rectangular prism = 2(length) x 3 (length) x 5 (length)
volume of rectangular prism = 2(1/2) x 3 (1/2) x 5 (1/2)
volume of rectangular prism = 1 x 3/2 x 5/2
volume of rectangular prism = 15/4
Therefore, the volume of the rectangular prism is 15/4.
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16) The cost, in dollars, of retaining the services of a computer repairman in Anchorville is given by
y = 42x + 32, where x is the number of hours worked
A) 32 signifies the hourly rate, and 42 signifies the overhead charge
B) 42 signifies the hourly rate, and 32 signifies the overhead charge
C) 74 signifies the cost for an on-site inspection
D) -42 signifies the hourly rate, and 32 signifies the travel cost
Answer:
B) 42 signifies the hourly rate, and 32 signifies the overhead charge
Step-by-step explanation:
The hourly rate is the amount of money given per hour worked. 42x basically means that for every hour, $42 are given.
As for 32, it is the overhead charge, which isn't paid every hour but rather only once. That is why it has no variable beside it.
Hope this helps!
The box plot shows ages of randomly sampled attendees at two different movies. Check all statements that apply to Movie A.
A) The range of the ages are greater
B) The ages are more consistent
C) The interquartile range is 15
D) The median ages of attendees are greater
Option B. is correct. Using box plot, the statement that apply to movie A is the ages are more consistent.
What is box plot?A box plot is "a special type of diagrams that shows quartiles in a box and the lines extending from the lowest to the highest value".
According to the question,
The box plot shows ages of randomly sampled attendees at two different movies.
The statement A. The range of the ages are greater. This statement is false because in the box plot movies A is range is 35 (subtract highest value from lowest value) that is not greater. Thus, this statement is false.Statement B. The ages are more consistent. This statement is true. To find consistency in box plot using hypotheses test we get consistency. Thus, the ages are more consistent. Statement C: Using value in box plot the interquartile range is Q₃ - Q₁. Where Q₃ - Q₁ = 42.5 - 17.5 = 25. Thus statement is false.Statement D: In box plot the median ages of attendees are greater. This statement is false.Hence, the ages are more consistent in box plot shows age of randomly sampled attendees at two different movies.
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Combine like terms to simplify the expression! Pls help me quick!!
Answer:
1/2 K-3/5
Step-by-step explanation:
2/5K simplifies to 4/10K. 4/10K+1/10K=5/10K. 5/10=1/2. 1/2K
K and 3/5 are not like terms so you can't combine them.
1/2K-3/5
Answer:
Step-by-step explanation:
add [tex]\frac{2}{5}k[/tex] with [tex]\frac{1}{10}k[/tex]
[tex]\frac{2}{5}k + \frac{1}{10}k = \frac{1}{2}k[/tex]
[tex]\frac{1}{2}k -\frac{3}{5}[/tex] and this is your answer
9. A person stands at the window of a building so that his eyes are 12.6 m above the level ground. An
object is on the ground 58.5 m away from the building on a line directly beneath the person. Compute
the angle of depression of the person's line of sight to the object on the ground.
Answer:
[tex]\theta = 12.16^0.[/tex]
Step-by-step explanation:
Given,
Height = 12.6 m
Object distance from the person = 58.5 m
Angle of depression
[tex]tan \theta = \dfrac{P}{B}[/tex]
[tex]tan \theta = \dfrac{12.6}{58.5}[/tex]
[tex]tan \theta = 0.2154[/tex]
[tex]\theta = 12.16^0[/tex]
Hence, angle of depression is equal to [tex]\theta = 12.16^0.[/tex]
The angle of depression of the person's line of sight to the object on the ground is 12.15°.
The information forms a right angle triangle. The person eyes above the ground is the opposite side of the triangle. The object distance from the building in line of the sight is the adjacent side of the right angle triangle.
Therefore,
using trigonometric ratio,
tan Ф = opposite /adjacent
tan Ф = 12.6 / 58.5
tan Ф = 0.21538461538
Ф = tan⁻¹ 0.21538461538
Ф = 12.1549416972
Ф = 12.15°
angle of depression ≈ 12.15°
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2. In a board game, you must roll two 6-sided number cubes. You can only start the game
if you roll a 6 on at least one of the number cubes. NOTE: This is using two cubes.
a. Make a list of all the different possible outcomes when two number cubes are
rolled (Sample Space) (2 points possible)
b. What fraction of the possible outcomes is favorable, or in other words, what is the
theoretical probability of rolling a 6 on at least one number cube when rolling
the two number cubes? (3 points possible) Hint: Highlight each pair in the
sample space that had at least one 6 in the outcome to help you identify
"favorable events
Answer:
A) Sample Space
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
B)Probability of rolling a 6
10/36
Step-by-step explanation:
Answer:
A. 1 2 3 4 5 6
1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
B. 11/36 or 0.3055555
Step-by-step explanation:
1. You can see there are 36 outcomes when rolling the dice.
2. Then you find that there are 11 possible outcomes with at least one 6. (For example 1-6 2-6 3-6.)
3. The chance of rolling at least one 6 in a pair of dice is 11/36.
4. 11 divided by 36 is 0.3055555.
(Though the calculator on Google says 0.305555556.)
why does the graph of an exponentai funcation have its shape
Please help me ASAP
Answer:
Two.
Step-by-step explanation:
Simultaneous equation is a Finite sets of equations whose common solutions are sought.
Two solutions in the equation above is sought.
Walter wants to learn more about the preferred salad ingredients of students in his
school. He surveys all students in his math class and finds that 4 prefer tomatoes,
14 prefer carrots, and 9 prefer cucumbers. What is the population and sample? Is
the sample a representative sample? Explain.
For example , If we want to calculate the average income of American data scientist , all American data scientists will be determine the population in this case,
A sample denotes a subset of population . When population is extremely large , the researcher draw a sample of the entire population and use this to analysis and study. So we can say a sample can represent a particular population.Here, Walter surveys all students in his math class and finds that 4 prefer tomatoes, 14 prefer carrots, and 9 prefer cucumbers.
Population = All students in his School
Sample = Students in his class.
No, the sample is not a representative sample, it is the convenience sample.
It can be possible that his class has influence of him or students of other classes may like exactly different ingredients for salad like sprouts, fruit etc.
Use the equation c = s + 10 to find the value of a when s = 2.
Answer:
C is 12
Step-by-step explanation:
You just add s "2" to 10.
Then you look and notice C is right next to the equal sign.
Finally, you have your answer of 12.
Graph the rational function. f(x )= x^2 - 7x + 10/x - 5
Answer:
x ≓ -1.425806820
Step-by-step explanation:
Answer:
Vertical Asymptotes: x=-4
Horizontal Asymptotes: y=1
What is the answer to this math question?
Answer:
The answer is option 3.
Step-by-step explanation:
First we have to find the area of both rectangle and triangle :
Rectangle,
[tex]area = base \times height[/tex]
Let base = 9,
Let height = 3,
[tex]area = 9 \times 3 \\ area = 27 \: {m}^{2} [/tex]
Triangle,
[tex]area = \frac{1}{2} \times base \times height[/tex]
Let base = 3,
Let height = 3,
[tex]area = \frac{1}{2} \times 3 \times 3 \\ area = \frac{1}{2} \times 9 \\ area = \frac{9}{2} \\ area = 4.5 \: {m}^{2} [/tex]
Lastly, in order to find the shaded region you have to substract the area of triangle from the area of rectangle :
[tex]area = 27 - 4.5 \\ area = 22.5 \: {m}^{2} [/tex]
Answer:
its 22.5 because i did a sguare then divivded it by 2 then i added the rectangle