Answer:
9.48
Step-by-step explanation:
Find the slope of the line y= -3x+7
Answer:
If you had a line of x = 7, (or any time you have an equation where x equals a number) then you would have a vertical line. In every vertical line, the slope is undefined. In equations of lines that are in the format of y = mx + b, the slope is represented by the "m".Answer:
-3
Explanation:
The given equation is in slope-intercept form. The format of slope-intercept is y = mx + b, where m is the slope and b is the y-intercept.
The slope is the coefficient of x.
In the equation y = -3x + 7, the slope is -3, because -3 is the coefficient of x.
Hence, the slope is -3.The shaded region R in diagram below is enclosed by y-axis, y = x^2 - 1 and y = 3.
Determine the volume of the solid generated when the shaded region R is revolved
about x = -1 by using Disk method.
Cross sections of the volume are washers or annuli with outer radii x(y) + 1, where
y = x(y) ² - 1 ==> x(y) = √(y + 1)
and inner radii 1. The distance between the outermost edge of each shell to the axis of revolution is then 1 + √(y + 1), and the distance between the innermost edge of R on the y-axis to the axis of revolution is 1.
For each value of y in the interval [-1, 3], the corresponding cross section has an area of
π (1 + √(y + 1))² - π (1)² = π (2√(y + 1) + y + 1)
Then the volume of the solid is the integral of this area over [-1, 3]:
[tex]\displaystyle\int_{-1}^3\pi y\,\mathrm dy = \frac{\pi y^2}2\bigg|_{-1}^3 = \boxed{4\pi}[/tex]
[tex]\displaystyle\int_{-1}^3 \pi\left(2\sqrt{y+1}+y+1\right)\,\mathrm dy = \pi\left(\frac43(y+1)^{3/2}+\frac{y^2}2+y\right)\bigg|_{-1}^3 = \boxed{\frac{56\pi}3}[/tex]
Find the intercepts for the graph of the equation.
-3x + y = 6
Answer:
y = 9
Step-by-step explanation:
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
What is the following product?(2square root 7 +3square root 6)(5square root2+4square root3)
Answer:
[tex]10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
Step-by-step explanation:
[tex]( 2 \sqrt7 + 3 \sqrt6)(5\sqrt2 + 4\sqrt3)\\\\= 2\sqrt7(5\sqrt2 + 4\sqrt3) + 3\sqrt6 ( 5\sqrt2 + 4\sqrt3)\\\\=10\sqrt{7 \times 2} + 8\sqrt{7 \times 3} + 15\sqrt{6 \times 2} + 12\sqrt{ 6\times 3}\\\\=10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{12} +12\sqrt{18}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{4 \times 3 } +12\sqrt{9 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{2^2 \times 3} +12\sqrt{3^2 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selection down to ten mysteries and twelve Nonfiction books. If she randomly chooses four books fro her selections, what’s the probability that they will all be nonfiction?
twelve nonfiction books. If she randomly chooses four books
answer to 4 decimal places, if necessary.
Answer
Answer:
0.0677 = 6.77% probability that they will all be nonfiction
Step-by-step explanation:
The books are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
10 + 12 = 22 books.
She chooses 4 books, which means that [tex]n = 4[/tex]
12 nonfiction, which meas that [tex]k = 12[/tex]
What’s the probability that they will all be nonfiction?
This is P(X = 4). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,22,4,12) = \frac{C_{12,4}*C_{10,0}}{C_{22,4}} = 0.0677[/tex]
0.0677 = 6.77% probability that they will all be nonfiction
Determine the degree of the polynomial:
7m^6n^5
9514 1404 393
Answer:
11
Step-by-step explanation:
The degree of the given monomial is the sum of the exponents of the variables.
m has degree 6
n has degree 5
The degree of the monomial is 6+5 = 11.
Given the following angles, what ray is the common side of CFD and ZDFE?
Answer:
B. Ray FD
Step-by-step explanation:
A common side of two angles is the side shared by the two angles. It is part of the sides that forms both angles.
The common side of <CFD and <DFE is therefore ray FD. Ray FD is part of the sides that forms <CFD and also <DFE.
Answer:
B. Ray FD
Step-by-step explanation:
A common side of two angles is the side shared by the two angles. It is part of the sides that forms both angles.
The common side of <CFD and <DFE is therefore ray FD. Ray FD is part of the sides that forms <CFD and also <DFE.
find the measure of angle BAC
Answer:
a= 26
Step-by-step explanation:
180-130=50
total angle in triangle =180
4a+a+50=180
then proceed like norma algebra
Lauren flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will
show heads, the spinner will land on green, and the cube will show an even number.
Lauren will get 2/25 because the coin only lands on heads or tail
Help. Does anyone know the answer. Pls help!
Answer:
Step-by-step explanation:
the first and last choices look good
Divide the following complex numbers:
[tex](2 + i) \div (1 - 4i)[/tex]
Answer:
[tex]-\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
Step-by-step explanation:
[tex] (2 + i) \div (1 - 4i) = [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} [/tex]
[tex] = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} [/tex]
[tex] = \dfrac{2 + 8i + i + 4i^2}{1 + 16} [/tex]
[tex] = \dfrac{2 + 9i - 4}{17} [/tex]
[tex] = \dfrac{-2 + 9i}{17} [/tex]
[tex]= -\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
Please answer & number. Thank you! <33
Answer:
2）=2
4）=3
5）=5
8）=-1
Step-by-step explanation:
just divide the number by the number with variable
When 50% of a number is added to the number, the results is 165
Answer:
this would look like
0.5x+x=165
1.5x=165
x=110
Hope This Helps!!!
A test taker gets 70 on 1st exam, 80 on 2nd exam, 2/3 of 4/5 of his 2nd exam on his 3rd test. If the professor gives 5 points extra credit on his 4th exam and his average score is 80, what was his score on the 4th exam
=================================================
Explanation:
The phrasing "2/3 of 4/5 of his 2nd exam on his 3rd test" is a bit clunky in my opinion. It seems more complicated than it has to be.
The student got 80 on the second exam. 4/5 of this is (4/5)*80 = 0.8*80 = 64. Then we take 2/3 of this to get (2/3)*64 = 42.667 approximately. If we assume only whole number scores are given, then this would round to 43.
Let x be the score on the fourth exam. Since 5 points of extra credit are given, the student actually got x+5 points on this exam.
So we have these scores
first exam = 70second exam = 80third exam = 43fourth exam = x+5Adding up these scores and dividing by 4 will get us the average
(sum of scores)/(number of scores) = average
(70+80+43+x+5)/4 = 80
(x+198)/4 = 80
x+198 = 4*80
x+198 = 320
x = 320 - 198
x = 122
So the student got a score of x+5 = 122+5 = 127 on the fourth exam.
The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the x-test statistic, and use the x-distribution to find the p-value of the test. Category Observed (Expected) A 25 (20) B 35(40) C 50(60) D 90(80) Round your answer for the chi-square statistic to two decimal places, and your answer for the p-value to four decimal places. chi-square statistic = p-value = i
Answer:
χ² = 4.80
Pvalue = 0.1874
Step-by-step explanation:
Given :
Category Observed (Expected)
A 25 (20)
B 35(40)
C 50(60)
D 90(80)
The Chisquare statistic (χ²) is given by :
χ² = Σ(observed - Expected)² / Expected
χ² = (25-20)²/20 + (35-40)/40 + (50-60)²/60 + (90-80)²/80
χ² = 1.25 + 0.625 + 1.67 + 1.25
χ² = 4.795
χ² = 4.80 (2 decimal places)
Using the Chisquare Pvalue calculator :
df = n - 1 = 4 - 1 = 3
Pvalue = 0.1874
the poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities.A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron.Formulate the linear programming model for this situation.
Answer:
- Min Z = $400C + $200A
Step-by-step explanation:
The linear programming model deals with the minimization or maximization of a linear function of several variables and inequalities. This method assists the industries in minimizing costs and maximizing production.
In the given situation,
The Linear programming model would be:
Min Z = $400C + $200 A
which is based on:
150 mg of vitamin K in corn C + 250 mg of vitamin K in AlfaAlfa ≥ 500
75 mg of iron in Corn + 50 mg of iron in AlfaAlfa ≥ 400
∵ C, A ≥ 0
Thus, the equation would be,
Min Z = $400C + $200 A
(3k + 5)(2k2 – 5k – 3)
How do I solve this?
Answer:
Step-by-step explanation:
4x+3y=13
5x-4y=-7
How do I solve this. Y=f(x)+a moves the function
Answer:
up
Step-by-step explanation:
for linear functions, adding a constant will increase the y value by two and shift the line up two units on the graph.
Answer: It moves the function 'a' units up if a > 0. Or it moves the function |a| units down if a < 0.
Explanation:
Consider an example like y = f(x)+2. This shifts the f(x) curve 2 units up because we're adding 2 to each y or f(x) output. A point like (5,7) shifts up to (5,9).
As another example, y = f(x)-5 moves the curve 5 units down.
In the first example, we had a > 0 which moved the function 'a' units up (a = 2 in that case). The second example had a = -5 which means a < 0, so that's why we shifted |a| = |-5| = 5 units down.
How much fabric is needed to make a tent in the shape of a triangular prism with the following measures?
Answer:
The fabric needs 196.4 ft²
Step-by-step explanation:
∵ The tent formed formed from 4 faces
two equilateral triangles with side length 7 ft
two rectangles with dimensions 11 ft and 7 ft
∵ Area equilateral Δ = 1/4 S²√3
∵ Area rectangle = L × W
∴ The area of the prism = 2 × 1/4 × (7)²√3 + 2 × 7 × 11
= 196.4 ft²
Note:
If you find the area of the triangle by the rule 1/2 × base × height
∴ Area Δ = 1/2 × (7) × 6 = 21 ft²
∴ Area tent = 2 × 21 + 2 × 77 = 196 ft²
Two answer very closed
Answer:
273 ft^2 (apparently you have to cover the ground)
Step-by-step explanation:
pls help
With a coupon you can buy up to 4 medium pizzas at $6 each. What is the
domain of this graph?
Answer:
Domain: {1, 2, 3, 4}
Step-by-step explanation:
The domain of the graph (input values) is the number of pizzas which are plotted on the x-axis while the range (output values) is the cost of pizza, plotted on the y-axis (vertical axis)
The domain therefore would consists of each x-coordinate that represent each point on the graph, which are {1, 2, 3, 4}
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 27 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order?
Answer:
9.5833333333 yd³
9 7/12 yd³
Step-by-step explanation:
23 * 27 * 5/12 = 258.75 ft³
1 yd³ = 3ft * 3ft * 3ft
1 yd³ = 27 ft³
258.75 ft³ * 1 yd³/27 ft³ = 9.5833333333 yd³
9.5833333333 yd³
9 7/12 yd³
Find the values of x and y
Answer:
d
Step-by-step explanation:
Answer:
x=5, y=52
Step-by-step explanation:
Hi there!
1) Determine y
Because length AB is equal to length BC (making this an isosceles triangle), angle y is equal to 52 degrees.
y = 52
2) Determine x
The sum of the interior angles of a triangle will always be 180 degrees. Knowing this, we can construct the following equation and solve for x:
[tex]180=52+52+(14x+6)[/tex]
Open up the parentheses
[tex]180=52+52+14x+6\\180=104+14x+6\\180=110+14x[/tex]
Subtract 110 from both sides to isolate 14x
[tex]180-110=110+14x-110\\70=14x[/tex]
Divide both sides by 14 to isolate x
[tex]\frac{70}{14} =\frac{14x}{14} \\5=x[/tex]
Therefore, the value of x is 5.
I hope this helps!
Here are the test scores for 8 students in Mr. M's class. 87, 55, 96, 38, 83, 64, 44, 81. What is the percentage of these test scores that are less than 84?
Answer:
75%
Step-by-step explanation:
Given that the score of 8 students in Mr. M's class are 87, 55, 96, 38, 83, 64, 44, 81, the scores less than 84 are 55, 38, 83, 64, 44, 81.
These means that 6 student had scores less that 84 of the 8 students hence the percentage of these test scores that are less than 84
= 6/8 * 100%
= 75%
This means that 75% of the students had scores less than 84
Find m angle NML; m angle QML=115^ and m angle NMQ=28^
Answer:
We're provided - m ∠ QML = 115° , m ∠ NMQ = 28° and we're asked to find out m ∠ NML. Set up an equation and solve for m ∠ NML.[tex] \large{ \tt{❀ \: m \: \angle \: NML= m \: \angle \:QML + m \: \angle \: NMQ}}[/tex]
[tex] \large{ \tt{⤇m \: \angle \:NML= 115 \degree + 28 \degree }}[/tex]
[tex] \boxed{ \large{ \tt{⤇ \: m \: \angle \:NML = 143 \degree }}}[/tex]
Hence , Our final answer is 143° . Hope I helped! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
A salesman receives a salary of RM 2000 per month. He wis receive a commission of RM 800 for each car he sells. If he sells n cars in a particular month,
a. Find his monthly salary when n = 18.
b. Express his salary in terms of n.
Answer:
a) month salary = RM(18×800+2000)
= RM 16400
b) his salary = RM(800n+2000)
Hope it helps
A regular hexagon has sides of 5 feet. What is the area of the hexagon? 12.5 ft 2 37.5 ft 2 25 ft 2 50 ft 2
Answer: [tex]37.5\sqrt{3}[/tex]
This value is exact. We can write this as 37.5*sqrt(3)
This approximates to roughly 64.9519
The units for the area are in square feet.
==========================================
Explanation:
Split the regular hexagon into 6 identical equilateral triangles.
Each equilateral triangle has side length x = 5 ft.
The exact area of one of the equilateral triangles is
A = 0.25*sqrt(3)*x^2
A = 0.25*sqrt(3)*5^2
A = 0.25*sqrt(3)*25
A = 0.25*25*sqrt(3)
A = 6.25*sqrt(3)
Multiply this by 6 to get the exact area of the regular hexagon.
6*A = 6*6.25*sqrt(3) = 37.5*sqrt(3) which is the exact area in terms of radicals or square roots.
If your teacher meant to say choice B is 37.5*sqrt(3), then that would be the final answer. If your teacher only said 37.5 without the sqrt(3) term, then there's a typo.
Need answers asap!!!!!!!!!!!!!!
Answer:
The answer is
x equal -243
Answer:
-243 is yr correct answer.
Step-by-step explanation:
(-3)^-5=1/x1/(-3)^5=1/x1/-243=1/xx= -243hope it helps
stay safe healthy and happy...Find the distance between the points (-5, -4) and (3, 1).
On a coordinate plane, points are at (3, 1), (negative 5, negative 4).
Step-by-step explanation:
it will help u
