Approximately [tex]\(8.51 \times 10^8\)[/tex] ice cream cones are purchased in one year, given a rate of 1.7 thousand cones per minute over [tex]\(5.3 \times 10^5\)[/tex] minutes.
To find the total number of ice cream cones purchased in one year, we can multiply the rate of purchase per minute by the total number of minutes in a year.
Given: Purchase rate = 1.7 thousand ice cream cones per minute, and there are [tex]\(5.3 \times 10^5\)[/tex] minutes in a year.
[tex]\[ \text{Total cones in one year} = \text{Rate per minute} \times \text{Minutes in a year} \][/tex]
[tex]\[ \text{Total cones} = 1.7 \times 10^3 \, \text{cones/minute} \times 5.3 \times 10^5 \, \text{minutes} \][/tex]
Now, multiply the coefficients and add the exponents:
[tex]\[ \text{Total cones} = 8.51 \times 10^8 \, \text{ice cream cones} \][/tex]
Therefore, approximately [tex]\(8.51 \times 10^8\)[/tex] ice cream cones are purchased in one year.
Final answer:
By multiplying 1.7 × 10³ cones per minute by 5.3 × 10⁵ minutes per year, the total number of cones purchased in one year is approximately 9.01 × 10⁸ cones.
Explanation:
To calculate the total number of ice cream cones purchased in one year, we can use scientific notation and multiplication. First, convert the number of ice cream cones bought per minute into scientific notation:
1.7 thousand cones per minute = 1.7 × 10³ cones/minute
Next, multiply this by the total number of minutes in a year, also given in scientific notation:
5.3 × 10⁵ minutes/year
The calculation will look like this:
(1.7 × 10³ cones/minute) × (5.3 × 10⁵ minutes/year) = (1.7 × 5.3) × (10³× 10⁵) = 9.01 × 10⁸ cones/year
The approximation for the number of cones purchased in one year is 9.01 × 10⁸ cones.
. A packing crate measures 0.40 m 0.40 m 0.25 m. You must fill the crate with boxes of cookies that each measure 22.0 cm 12.0 cm 5.0 cm. How many boxes of cookies can fit into the crate?
Answer:
The answer to your question is: 30 boxes
Step-by-step explanation:
Data:
A packing crate measures 0.40 m 0.40 m 0.25 m.
boxes of cookies measure 22.0 cm 12.0 cm 5.0 cm
Formula
Volume of a rectangular prism: l x w x h
Volume of the bigger prism = 40 cm x 40 x 25 cm = 40 000 cm3
Volume of the smaller prism = 22 x 12 x 5 = 1320 cm3
Then we divide the volumes = 40000 / 1320 = 30.3 boxes
On another day, Martin bought 12 3/5 pounds of grapes for a picnic. His friend bought 3/8 of that amount. Use compatible fractions to estimate how many pounds of grapes Martin's friend bought.
Answer:
12 1/2
1/2
6 1/4
Step-by-step explanation:
hope this helps ya
To estimate Martin's friend's purchase of grapes, convert 12 3/5 to an improper fraction and multiply it by 3/8. The estimate is 9/40 pounds of grapes.
Explanation:To estimate how many pounds of grapes Martin's friend bought, we can use compatible fractions. Martin bought 12 3/5 pounds of grapes. His friend bought 3/8 of that amount.
Step 1: Convert 12 3/5 to an improper fraction.
12 3/5 = (5 * 12 + 3)/5 = 63/5
Step 2: Multiply the improper fraction by 3/8.
(63/5) * (3/8) = (63 * 3)/(5 * 8) = 9/40
Therefore, Martin's friend estimated about 9/40 pounds of grapes.
Divide. (4x^2+27x+22) dived by (x+6) your answer should give the quotient and remainder.
Answer:
quotient = 4x + 3 + (3/x+6)
Step-by-step explanation:
To solve this, we conduct polynomial division. We divide the first term of the divisor into the first term of the polynomial.
Step 1: Divide the first term of the polynomial, 4x^2, by the first term in the divisor, x, to obtain 4x. This is the first term of our quotient.
Step 2: Keep the divisor, x+6, as it is and multiply it by the first term of the quotient, 4x. We obtain 4x^2 + 24x.
Step 3: Subtract this result from the original polynomial. The difference is 3x+22.
Step 4: The divisor x+6 is then divided into the first term of the new polynomial, 3x, to obtain 3. Add this to the quotient, making the quotient 4x+3.
Step 5: Multiply the divisor, x+6, by the new term in the quotient, +3, obtaining 3x+18.
Step 6: Subtract this result from the last polynomial, 3x+22, to get the remainder, 4
So when we divide 4x^2 +27x+22 by x+6, we get the quotient is 4x+3 and the remainder is 4.
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Please help me with this problem
Answer:
y = - 2x
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = - 5, y = 10, thus
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{-5}[/tex] = - 2, hence
y = - 2x ← is the equation relating them
A class of fourth graders takes a diagnostic reading test and the scores are reported by reading level. The 5-number summaries for the 14 boys and 11 girls are shown:
Boys: 2.0, 3.9, 4.3, 4.9, 6.0
Girls: 2.8, 3.8, 4.5, 5.2, 5.9
Which group generally did better on the test?
Answer:
The girls had a higher average in the reading test than the boys.
Step-by-step explanation:
To find the solution, you need to find the mean (average) of the group of boys and group of girls each. The mean of numbers can be found by dividing the sum of all numbers by the amount of numbers there are.
Lets start by finding the mean of the boys group. Find the sum of all numbers:
[tex]2.0 + 3.9 + 4.3 + 4.9 + 6.0 = 21.1[/tex]
Now divide the sum by how many numbers, or in this case, how many boys did the test:
[tex]21.1 \div 5 = 4.22[/tex]
The mean, average, of the tests conducted by the group of boys is 4.22.
Repeat the same for the girls group:
[tex]2.8 + 3.8 + 4.5 + 5.2 + 5.9 = 22.2 \\ 22.2 \div 5 = 4.44[/tex]
The mean, average, of the tests conducted by the group of girls is 4.44.
Compared to 4.22, 4.44 is bigger than 4.22.
x 3 +25x 2 +50x−1000 spacex, start superscript, 3, end superscript, plus, 25, x, start superscript, 2, end superscript, plus, 50, x, minus, 1000 The polynomial above has (x-5)(x−5)left parenthesis, x, minus, 5, right parenthesis and (x+10)(x+10)left parenthesis, x, plus, 10, right parenthesis as factors. What is the remaining factor?
The remaining factor of the given polynomial x^3 + 25x^2 + 50x - 1000, knowing that (x-5) and (x+10) are factors, is 'x - 20'. This is calculated by dividing the original polynomial by the known factors.
Explanation:In the polynomial
x^3 + 25x^2 + 50x - 1000
, you have expressed that (x-5) and (x+10) serve as factors. Thus, to find the remaining factor, we need to divide the polynomial by these two known factors. We'll begin with dividing the original polynomial by (x-5). This yields a quotient of x^2 + 20x - 200. Subsequently, we divide this quotient by the second known factor (x+10), which ultimately gives us the final factor, being
x - 20
. Hence, x - 20 is the remaining factor of the polynomial.
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Tatsu drew a scale drawing of a campground. The scale he used was 1 inch : 5 yards. In the drawing, the picnic area is 19 inches long. What is the length of the actual picnic area?
Answer:
The answer to your question is: 95 yards
Step-by-step explanation:
Data
1 inch ---------------- 5 yards
19 inches ------ ? yards
We can solve this problem with a rule of three
1 inch ------------------ 5 yards
19 inches -------------- x
x = (19)(5) / 1 = 95 yards
Answer:
it was wrong!!
Step-by-step explanation:
Vector A⃗ has magnitude 5.00 and is at an angle of 36.9∘ south of east. Vector B⃗ has magnitude 6.40 and is at an angle of 20.0∘ west of north. Choose the positive x-direction to the east and the positive y-direction to the north. Find the components of A⃗ .
Final answer:
The x-component of vector A is 4.00 units east, and the y-component of vector A is -3.00 units south, calculated using the cosine and sine functions respectively.
Explanation:
The student has asked for the components of vector A which has a magnitude of 5.00 units and is at an angle of 36.9° south of east. To find the components of a vector, we use trigonometric functions. The component along the x-axis (east-west direction) is found using the cosine function, and the component along the y-axis (north-south direction) is found using the sine function. Since the angle is south of east, the x-component will be positive and the y-component will be negative in our coordinate system.
The x-component of vector A (Ax) is calculated as:
Ax = A * cos(θ) = 5.00 * cos(36.9°) = 5.00 * 0.800 = 4.00 units
The y-component of vector A (Ay) is calculated as:
Ay = A * sin(θ) = 5.00 * sin(36.9°) = 5.00 * 0.600 = 3.00 units
Therefore, the components of vector A are 4.00 units east and -3.00 units south.
Point G is on segment FH such that it partitions segment FH into a ratio of 2:3.Point F is located at (5, 7) and point H is located at (16, 13). What are the coordinates of point G?
Answer:
G = (9.4, 9,4)
Step-by-step explanation:
The ratio is applied in the x-distance and the y-distance. The ratio is 2:3 so you have to divide the distances by 5 and 2/5 correspond to FG and 3/5 to GH
x-distance:
x2 - x1 = 16 - 5 = 11
11/5 = 2.2
y-distance:
y2 - y1 = 13 - 7 = 6
6/5 = 1.2
Point G = Point F + (2.2*2, 1.2*2)
Point G = (5, 7) + (4.4, 2.4)
= (9.4, 9.4)
The current value of a property is $40,000. The property is assessed at 40% of its current value for real estate tax purposes, with an equalization factor of 1.5 applied to the assessed value. If the tax rate is $4 per $100 of assessed, what is the amount of tax due on the property?
Answer:
Tax due on the property : $ 960
Step-by-step explanation:
We know that the property is assessed at the 40% of it's current value.
First we are going to find the value assessed.
40% of $40,000 = 0.4 * 40,000 = $ 16,000
Now, at the value, we are aplying a factor of 1.5. This equalization factor is the multiplier we use to calculate the value of a property that is in line with statewide tax assessments
So, we do, 1.5* $16,000 = $24,000
Now we got that we the tax rate is $4 per $100 assessed.
So we got $24,000 * $4 / $100 = $ 960
If F(x) = 5x/(1 + x2), find F '(2) and use it to find an equation of the tangent line to the curve y = 5x/(1 + x2)at the point (2, 2).
Answer:
3x+5y-16=0
Step-by-step explanation:
See it in the pic.
Equation of tangent line to the curve is
[tex]y=-\frac{3}{5}x+\frac{16}{5}[/tex]
Tangent line to the curve.Equation of tangent line is in the form of y=mx+b
where m is the slope and b is the y intercept
Derivative :Derivative of a given function is the slope. To find slope at the given point , we find out f'(2)
we are given with function
[tex]f(x)= \frac{5x}{1+x^2} \\Apply \; quotient \; rule \\5\frac{\frac{d}{dx}\left(x\right)\left(1+x^2\right)-\frac{d}{dx}\left(1+x^2\right)x}{\left(1+x^2\right)^2}\\5\cdot \frac{1\cdot \left(1+x^2\right)-2xx}{\left(1+x^2\right)^2}\\\frac{5\left(1-x^2\right)}{\left(1+x^2\right)^2}\\[/tex]
Now we find f'(2) by replacing 2 for x
[tex]f'(x)=\frac{5\left(1-x^2\right)}{\left(1+x^2\right)^2}\\f'(2)=\frac{5\left(1-2^2\right)}{\left(1+2^2\right)^2}\\f'(2)=\frac{-15}{25} \\f'(2)=-\frac{3}{5}[/tex]
Now we use the given point and the slope to get the equation of tangent line
[tex]m=-\frac{3}{5} and (2,2)\\y-y_1=m(x-x_1)\\y-2=-\frac{3}{5}(x-2)\\y-2=-\frac{3}{5}x+\frac{6}{5}\\y=-\frac{3}{5}x+\frac{6}{5}+2\\y=-\frac{3}{5}x+\frac{16}{5}[/tex]
Equation of tangent line to the curve is
[tex]y=-\frac{3}{5}x+\frac{16}{5}[/tex]
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Pastries made out of filo dough and brushed with either olive oil or butter (but not both). Pastries made out of shortcrust dough are not brushed with anything. Rashid and Mikhail submitted a total of x pastries to a baking competition. Mikhail used filo dough for all of his pastries, Rashid used shortcrust dough for all of his pastries, and each pastry was made using only one kind of dough. If Rashid made 2323 as many pastries as Mikhail, and 5858 of the filo dough pastries were brushed with olive oil, then how many of the pastries submitted by Rashid and Mikhail, in terms of x, were brushed with butter?
A. 3X203X20
B. 9X409X40
C. 1X41X4
D. 3X83X8
E. 5X12
Answer:
[tex]\frac{9x}{40}[/tex] is the answer.
Step-by-step explanation:
The question has some typo errors.
Rashid and Mikhail submitted a total of x pastries to a baking competition.
Suppose say :
Mikhail made x pastries .
Hence Rashid made [tex]\frac{2x}{3}[/tex] pastries.
And in total they made [tex]\frac{5x}{3}[/tex] pastries.
Now we have that out of x, [tex]\frac{5}{8}[/tex] of x were brushed with olive oil.
So, [tex]\frac{3}{8}[/tex] of x that is [tex]\frac{3x}{8}[/tex] are brushed by butter.
So, it becomes [tex](\frac{3}{8}) / ( \frac{5x}{3} )[/tex]
= [tex]\frac{3}{8} \times\frac{3x}{5}[/tex] = [tex]\frac{9x}{40}[/tex]
Hence, answer is option B.
Simplify the expression (4 + 5i)(4 - 5i).
16 - 20i
16 + 20i
-9
41
The expression (4 + 5i)(4 - 5i) simplifies to 41, as the multiplication of complex conjugates yields a real number.
The expression (4 + 5i)(4 - 5i) is a product of two complex conjugates. When multiplied, the product of complex conjugates results in a real number because the imaginary parts cancel out. The multiplication proceeds as follows:
Multiplying the real parts: 4 * 4 = 16.
Multiplying the outer terms: 4 * (-5i) = -20i (but this will cancel out with the next step).
Multiplying the inner terms: 5i*4 = 20i (which cancels out the -20i from the outer multiplication).
Multiplying the imaginary parts: 5i * -5i = -25[tex]i^2[/tex]. Remembering that i^2 = -1, we simplify this to -25 * -1 = 25.
Adding the results from steps 1 and 4, we get 16 + 25 = 41.
Therefore, the simplified expression is 41.
Among undergraduate students living on a college campus, 20% have an automobile. Among undergraduate students living off campus, 60% have an automobile. Among undergraduate students, 30% live on campus. Given the probabilities of the following events when a student is selected at random:
(a) Student lives off campus.
(b) Student lives on campus and has an automobile.
(c) Student lives on campus and does not have an automobile.
(d) Student lives on campus and/or has an automobile.
(e) Student lives on campus given that he/she does not have an automobile.
Answer: a) 70%
b) 6%
c) 24%
d) and: 6%
or: 66%
e) 46.2%
Step-by-step explanation:
Living on campus = 30%
Living off Campus = 70%
Living on campus with car = 20% of 30% = 0.2 x 0.3 = 0.06 = 6%
Living on campus w/o car = 80% of 30% = 0.8 x 0.3 = 0.24 = 24%
Living off campus with car = 60% of 70% = 0.6 x 0.7 = 0.42 = 42%
Living off campus w/o car = 40% of 70% = 0.4 x 0.7 = 0.28 = 28%
a) 70%
b) 6%
c) 24%
d) Student lives on campus and has an automobile: 6%
Student lives on campus or has an automobile = 66%
living on campus 30%
students with car = 6% (on campus) 42% (off campus)
30 - 6 + 42 = 66
e) P (living on campus/not have a car) = P(living on campus w/o a car)/P(not have a car)
P(living on campus w/o a car) = 24
P(not have a car) = 24+28 = 52
P (living on campus/not have a car) = 24/52 = 0.462 = 46.2%
The graph below shows the time Andrea spent reading one day. Write a few sentences to describe the relationship between the time Andrea spent reading and the number of pages she read.
Answer:
Step-by-step explanation:
Well, there are several relationships you can describe. As time increases how does number of pages react? Like does it increase or decrease. Is it always increasing or decreasing by the same amount? If it's not all the same how do different parts look different.
There aren't any actual numbers, so you can't say specifically how they relate, like you can't say she read 5 pages a minute or something.
There is no smooth increase or decrease of the graph thus it reperesnts a non linear relationship.
What does it mean when a graph does not increase or decrease smoothly?Typically, when a graph increases or decreases abruptly, the data or function it represents is showing some sort of discontinuity or sudden change in behavior.
In other words, there are areas or locations on the graph where values or the slope abruptly shift rather than gradually and constantly changing.
Thus, the slope of the graph is constantly changing and the relationship that is depicted is non linear.
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How can you determine the coordinates of any image that is dilated with the center of dilation at the origin without graphing? Explain your reasoning.
Answer:
See explanation
Step-by-step explanation:
Let [tex](x,y)[/tex] be the coordinates of the point which has to be dilated with the scale factor of [tex]k[/tex] with the center of dilation at point [tex](0,0)[/tex] (the origin).
The dilation with the scale factor [tex]k[/tex] and the center of dilation at the origin has the rule
[tex](x,y)\rightarrow (kx,ky)[/tex]
So, you have simply to multiply each coordinate of the point by [tex]k[/tex] to get the image's coordinates.
Help me please!!!!!!!!!!
Answer:
slope: -5/3y-intercept: 2x-intercept: 6/5 = 1.2Step-by-step explanation:
Finding the slope is perhaps easiest done by solving for y.
5x -6 = -3y . . . . subtract 3
y = -5/3x +2 . . . divide by -3
This is slope-intercept form, so we can see both the slope (the coefficient of x, -5/3) and the y-intercept (the constant, +2).
__
To find the x-intercept, we set y=0 and solve for x. This might be most easily done using the original equation:
5x -3 = 0 +3 . . . . set y = 0
5x = 6 . . . . . . . . . add 3 to get the x-term by itself
x = 6/5 = 1.2 . . . . divide by the coefficient of x. This is the x-intercept.
__
Slope = -5/3
y-intercept = 2
x-intercept = 6/5
Is my answer correct?
Answer:
[tex]2 = x[/tex]
Step-by-step explanation:
THIS IS CORRECT! These two angles are somewhat linear pairs, so you set both expressions equal to 180°:
[tex]180° = 52° + (2^{3x + 1})°[/tex]
- 52° - 52°
______________________
128° = [tex](2^{3x + 1})°[/tex]
7 = 3x + 1
-1 - 1
_______
[tex]\frac{6}{3} = \frac{3x}{3} \\ \\ 2 = x[/tex]
[tex]128° = [2^7]°[/tex]
I am joyous to assist you anytime.
Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?
Answer:
[tex]\frac{2}{5}*\frac{3}{5} +\frac{2}{5}*\frac{2}{5}+\frac{3}{5} *\frac{3}{5} = \frac{19}{25}[/tex]
Step-by-step explanation:
We must remember that in order to get one even number we need to multiply one even number times one odd number or two even numbers. So, the first term tells the probability of having an even number from A and an even number from B, the next would be even from A and odd from B and the last one tells the likelihood of having odd from A and even from B
Write an equation in point-slope form for the line that passes through each point with the given slope.
1. (2,2), m = -3
2. (1,-6), m =-1
3. (-3,-4), m=0
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})~\hspace{10em} \stackrel{slope}{m}\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{0}[x-\stackrel{x_1}{(-3)}]\implies y+4=0(x+3) \\\\\\ y+4=0\implies y=-4[/tex]
When triangle ABC is similar to triangle PQR, with A, B, and C corresponding to P, Q, and R, respectively, it is customary to write ABC ∼ PQR. Suppose that AB = 4, BC = 5, CA = 6, and RP = 9. Find PQ and QR.
Answer:
PQ = 6 and QR = 7.5
Step-by-step explanation:
The lengths of the sides of two similar triangles are proportional. That is, if Δ ABC is similar to Δ PQR, then the following equation is established.
[tex]\frac{AC}{PR}=\frac{AB}{PQ}=\frac{BC}{QR}[/tex]
[tex]\frac{6}{9} = \frac{4}{PQ} = \frac{5}{QR}[/tex]
[tex]\frac{6}{9} = \frac{4}{PQ}[/tex]
PQ = 6
[tex]\frac{6}{9} = \frac{5}{QR}[/tex]
QR = 7.5
The factorization of x2 + 3x – 4 is modeled with algebra tiles. An algebra tile configuration. 2 tiles are in the Factor 1 spot: 1 is labeled + x, 1 is labeled negative. 5 tiles are in the Factor 2 spot: 1 is labeled + x and 4 are labeled +. 10 tiles are in the Product spot: 1 is labeled + x squared, 1 is labeled negative x, the 4 tiles below + x squared are labeled + x, and the 4 tiles below the negative x tiles are labeled negative. What are the factors of x2 + 3x – 4?
Final answer:
The factorization of x² + 3x - 4 is (x + 4)(x - 1), which can be verified using algebra tiles that represent these factors and the product.
Explanation:
The factors of x² + 3x - 4 can be determined by looking for two numbers that multiply to -4 (the constant term) and add up to +3 (the coefficient of the middle term x). Through factor pairs of -4 (e.g., -1 and 4, or 2 and -2), we notice that (+4) and (-1) are the numbers that meet the criteria because 4 × (-1) = -4 and 4 + (-1) = 3. Therefore, the factorization is (x + 4)(x - 1). To use algebra tiles, you would arrange them into a rectangle where the length and width represent the factors of the quadratic expression, and the product area represents the entire expression.
Given y inversely proportional to x and x = 3 for y=6, what is x if y = 9?
02
0
4.5
0
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4.5 Is the answer required
Answer: 2
Step-by-step explanation: got it right :)
Rebecca went swimming yesterday. After a while she had covered one fifth of her intended distance. After swimming six more lengths of the pool, she had covered one quarter of her intended distance. How many lengths of the pool did she intend to complete?
A. 40
B. 72
C. 80
D. 100
E. 120
Answer:
Option E.
Step-by-step explanation:
Let the intended length of Rebecca's swimming is = x units
and we assume the length of the pool = l units
Now it is given in the question that " She covers one fifth of her intended distance "
That means distance covered = [tex]\frac{x}{5}[/tex]
" After swimming six more lengths of the pool she had covered one quarter of her intended distance"
So [tex]\frac{x}{5}+6(l)=\frac{x}{4}[/tex]
[tex]6l=\frac{x}{4}-\frac{x}{5}[/tex]
[tex]6l=\frac{x}{20}[/tex]
x = 20×(6l)
x = 120l
Therefore, Rebecca has to complete 120 lengths of the pool.
Option E is the answer.
The midpoint of segment XY is (6, -3). The coordinates of one endpoint are X(-1, 8). Find the coordinates of endpoint Y.
Answer:
The answer to your question is: Y = (13, -14)
Step-by-step explanation:
Data
midpoint = mp = (6, -3)
one endpoint = X = (-1, 8)
second endpoint = Y = (x, y)
Formula
Xmp = (x1 + x2) / 2
Ymp = (y1 + y2) / 2
Process
x2 = 2xmp - x1
y2 = 2ymp - y1
x2 = 2(6) - (-1) y2 = 2(-3) - 8
x2 = 12 + 1 y2 = -6 - 8
x2 = 13 y2 = - 14
Y = (13, -14)
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The sales representative made a deal with the schools for a discount on the individual juice bottles. The company usually sells the bottles to the distributors for $2.25, but they are selling them to the schools for 15% off. For what price will they sell each bottle to the schools?
-the answer is they will sell them to the schools for $1.91 per bottle.
just explain correctly plz how to get the answer
Answer:
$1.91
Step-by-step explanation:
This means the cost of the item to you is $1.91. You will pay $1.91 for a item with original price of $2.25 when discounted 15%. In this example, if you buy an item at $2.25 with 15% discount, you will pay 2.25 - 0.3375 = 1.91 dollars.
Answer:
1.91
Step-by-step explanation:
1- 2.25
2- 2.25÷100= 0.0225 find 1 percent
3- 0.0225×15=0.3375 find the 15 percent
4- 2.25-0.3375=1.9125 subtract the discount of the original price
5- 1.91 round off to two decimals
which equation is the equation of the line, in point-slope form, that has a slope of 1.9 and passes through the point (4.5, -1.4) ?
Answer:
y+1.4=1.9 (x-4.5)
Step-by-step explanation:
The slope is the number in front of the brackets, which must be positive 1.9. This eliminates the last option. It is y+1.4 because the formula is y-y1=m (x-x1)
So once you substitute values
y--4.5=1.9 (x-4.5)
y+4.5=1.9 (x-4.5)
An equation of the line in point-slope form is: B. y + 1.4 = 1.9(x - 4.5)
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (4.5, -1.4) and a slope of 1.9, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-1.4) = 1.9(x - 4.5)
y + 1.4 = 1.9(x - 4.5)
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Standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers. How many different standard plates are possible in this system? (Assume repetition of letters and numbers is allowed.)
Answer: 175760000
Step-by-step explanation:
We know that the total number of digits in the number system is 10 [0,1,2,3,4,5,6,7,8,9]
The total number of letters in English Alphabet = 26
Now, if standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers, then the number of different standard plates are possible in this system (if repetition of letters and numbers is allowed)will be :_
[tex]= 10\times10\times26\times26\times26\times10\times10\\\\=175760000[/tex]
Hence, the number of different standard plates are possible in this system = [tex]175760000[/tex]
In the given license plate system, there are 175,760,000 possible combinations by calculating the combinations for each segment (2 numbers, 3 letters, 2 numbers) and multiplying them together.
A standard automobile license plate in this system consists of 2 numbers, followed by 3 letters, followed by 2 numbers. To determine the number of different plates possible, we calculate the combinations for each part separately and then multiply them together.
Two Numbers: Each number can be any digit from 0-9, which gives us 10 possibilities for each digit. Therefore, the total combinations for the two numbers are: 10 x 10 = 100.Three Letters: Each letter can be any from the 26 English alphabets (A-Z). Thus, the total combinations for the three letters are: 26 x 26 x 26 = 17,576.Two Numbers: Similar to the first part, we have another set of two numbers with 10 possibilities each. Hence, the combinations for these two numbers are: 10 x 10 = 100.To find the total number of different standard license plates possible, we multiply the combinations for each part:
Total Plates = 100 x 17,576 x 100 = 175,760,000
Therefore, there are 175,760,000 different possible license plates in this system.
A company reported $50,000 net cash provided by operating activities. It invested $1,000 in equipment and paid $1,000 in dividends. Its free cash flow was a) $44,000. b) $52,000. c) $48,000. d) $12,000.
Answer:
The answer is c. $48,000
Step-by-step explanation:
To find the free cash flow, we need to take into account the money that is entering the company and the money that is being used. Money that we are earning is possitive, and money being spend goes with a minus.
The net cash, the $50,000 is our sales column. And is money entering the company.
The Investment would be our CAPEX or directly we can use it as investment. And this money is being spended.
The dividends, are the payments that we are doing to the board of directors or the share holders. Since we are paying others, we know this money is being used.
The equation here is:
Sales - Investment - Dividends = Free Cash Flow
So it $50,000 - $1,000 - $1,000 = $48,000
Consider this bag of marbles. What is the probability of drawing a green marble versus the ODDs of drawing a green marble? What is the difference in these two things? Make sure you show work, answer all questions, and write in complete sentences.
Answer:
Probability: 50%
odds: 5:5
Step-by-step explanation:
Answer:
The probability is 50% that ball will be green.
Odds 5:5
Numbers of ways to draw a green marbles: number of ways to draw another marbles.
Step-by-step explanation:
Consider the provided bag of marble.
The bag contains 5 green marble, 3 blue marbles and 2 red marbles.
The total number of marbles are: 5+3+2=10
The probability of getting a green marble is: 5/10=0.5
That means the probability is 50% that ball will be green.
Drawing green marbles means we want marble should be green and ODDs of drawing a green marble means the marble is not green.
There are 5 green marbles, so there are 5 outcomes that we want (out of 10 outcomes total)
There are 10-5 = 5 outcomes that we don't want a green marble.
Number of outcomes we want is 5
Number of outcomes we don't want is 5
Odds in favor = (wanted outcomes):(unwanted outcomes)
Odds in favor = 5:5
Numbers of ways to draw a green marbles: number of ways to draw another marbles.