Answer:
[tex]\mathbf{V = \dfrac{2}{3}}[/tex]
Step-by-step explanation:
Consider the tetrahedron enclosed by the coordinate planes and the plane 2x + y + z = 2
Let A be the region obtained by projecting the volume(V) onto the xy-plane.
Similarly, the plane 2x + y + z = 2 intersects with the xy-plane in y = 2 - 2x.
Using the vertical strips, the region A is to the xy-plane can be expressed as:
[tex]A = \{(x,y) | 0 \le x \le 1, 0 \le y \le 2 - 2x\}[/tex]
Thus, the volume of the solid can be calculated as follows;
[tex]V = \int^1_0 \int ^{2-2x}_{0} \int ^{2-2x-y}_{0} \ dz \ dy \ dx[/tex]
[tex]V = \int^1_0 \int ^{2-2x}_{0} (2-2x-y) \ dy \ dx[/tex]
[tex]V = \int^1_0 \bigg [2\times y -2x\times y - \dfrac{y^2}{2} \bigg]^{2-2x}_{0} \ dx \[/tex]
[tex]V = \int^1_0 \bigg [2\times (2-2x) -2x\times (2-2x) - \dfrac{(2-2x)^2}{2} \bigg]\ dx[/tex]
[tex]V = \int^1_0 \bigg [2x^2-4x+2 \bigg]\ dx[/tex]
[tex]V = \bigg [2\dfrac{x^3}{3}-\dfrac{4x^2}{2}+2 x\bigg]^1_0[/tex]
[tex]V = \bigg [2\dfrac{(1)^3}{3}-\dfrac{4(1)^2}{2}+2 (1)-0\bigg][/tex]
[tex]V = \dfrac{2}{3}- 2 + 2[/tex]
[tex]\mathbf{V = \dfrac{2}{3}}[/tex]
Sophia can spend at most $50 on clothes. Which inequality represents this situation?
Answer:
x ≤ 50
I hope this was helpfull :)
I WILL MARK BRAINIEST
I got one correct there should be about one more that’s also right
So essentially an adjacent angle is when two angles have a common side and a common vertex.
So knowing that we can determine from the picture all the adjacent angles:
D) <2 and <3 are adjacent angles
E) <1 and <3 are adjacent angles
F) <1 and <5 are adjacent angles
I hope this helps.
subtract the difference of d and c from 2
Please help me I’m giving brainliest and I need help
Answer:
c is the answer
Step-by-step explanation:
Answer:
A NUMBER
Step-by-step explanation:
8.Convert the line into slope intercept form: 3x + 5y =-15
Answer:
Y= -3/5x - 3
Step-by-step explanation:
3x+5y=-15
-3x. -3x
5y=-3x-15 then you would divide 5 from all the numbers to get : y=-3/5x-3.
help⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️
Step-by-step explanation:
Hope this helps, happy learning
3x+2y=5 from.a given equation, find two points that will satisfy the equation
Answer:
(0,2.5) and (1,1)
Step-by-step explanation:
Given
[tex]3x + 2y = 5[/tex]
Required
Determine the points that satisfy the equation
To do this, we substitute values for x and y in the equation.
Let x = 1
Substitute 1 for x in [tex]3x + 2y = 5[/tex]
[tex]3(1) + 2y = 5[/tex]
[tex]3 + 2y = 5[/tex]
Make 2y the subject
[tex]2y = 5 - 3[/tex]
[tex]2y = 2[/tex]
Solve for y
[tex]y = 1[/tex]
Hence, a point is: (1,1)
To determine another point, take x as 0
Substitute 0 for x in [tex]3x + 2y = 5[/tex]
[tex]3(0) + 2y = 5[/tex]
[tex]0 + 2y = 5[/tex]
[tex]2y = 5[/tex]
Solve for y
[tex]y = \frac{5}{2}[/tex]
[tex]y = 2.5[/tex]
Hence, another point is (0,2.5)
if the side ratio is 9:12, then the volume ratio is
Find the missing values for each of the following 3 questions
1. 90% of _____= 9
2. 55% of _____= 33
3. 30% of _____= 24
Paul get 5$ week for doing his chores he is saving his money to buy a skateboard that cost 85$ he has already saved 5$
Answer:
16 weeks
Step-by-step explanation:
85 divided by 5 is 17. Take away one week for the $5 he already has. So you get 16 weeks.
Hope this helps you!
when adding two rational numbers tell what the sign of the sum will be if one rational number is positive and one is negative
Answer:
True
When you add two negative numbers the sum is always negative ex.
When you add two numbers with different signs get the difference and get the sign by the larger absolute value ex.
Step-by-step explanation:
What is the probability that the average of four babies' weights will be within 0.6 pounds of the mean; will be between 7.4 and 8.6 pounds
Answer:
.682
Step-by-step explanation:
Which of the following describes how to calculate net pay?
A)Subtract the total deductions from the net pay.
B)Add the total deductions to the gross pay.
C)Subtract the total deductions from the gross pay.
D) Subtract the total deductions from the take-home pay.
Answer: C
Step-by-step explanation: The answer is C because it is.
which integer is greater.
l-5l or l3l
Answer:
|-5|
Step-by-step explanation:
When you see the absolute value signs and a number in between, that number is always going to be the positive version of that number (if the number is already positive, it stays positive)So, |-5| = 5, and 5 is greater than 3, therefore |-5| is greater than |3|I hope this helps!
Evaluate the expression when t is 4.
Answer:
t=4
Step-by-step explanation:
there nothing more to do
Answer:
its 4 i think
Step-by-step explanation:
|x| = 4 This means: What value can we substitute for x to get an answer of 4?
**You might automatically say: x = 4 because |4| = 4
Yes, you are correct! However, this is not the only answer. You will have two answers for this equation because:
Isn't |-4| = 4 ?
So, this answer is x = 4 or -4.
Find the value of X, I need help solving this
Answer:
the answer should be c
Step-by-step explanation:
180-90=90
90-41=49
49-1=48
48:6=8
x=8
Answer:
C) 8
Step-by-step explanation:
41 + 6x + 1 = 90° because this is a right angle
42 + 6x = 90 subtract 42 from both sides
6x = 48 divide both sides by 6
x = 8
LCM of a2+b2 and a4-b4
Answer:
The LCM is:
[tex](a^2+b^2)(a+b)(a-b)[/tex]
Step-by-step explanation:
Given polynomials are:
[tex]a^2+b^2\\a^4 - b^4[/tex]
We can use factorization to find the LCM of the given polynomials.
Taking the second polynomial, using the identity
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
Applying on 2nd polynomial
[tex](a^2)^2-(b^2)^2\\=(a^2+b^2)(a^2-b^2)\\=(a^2+b^2)(a+b)(a-b)[/tex]
We can see that [tex]a^2+b^2[/tex] is common in both polynomials, it will be counted only one time. The LCM of given polynomials is:
[tex](a^2+b^2)(a+b)(a-b)[/tex]
Find the measure of each acute angle.
(19x - 1)
(13x - 5)
(193' - 1) =
and (132 – 5)° =
Answer:
(19x - 1)° = 56°
(13x - 5)° = 34°
Step-by-step explanation:
Property of the interior angles of a triangle:
Sum of interior angles of a triangle is 180°.
Therefore, sum of angles of the given right triangle will be,
(19x - 1)° + (13x - 5)° + 90° = 180°
32x - 6 + 90 = 180
32x = 96
x = 3
(19x - 1)° = 19×3 - 1 = 56°
(13x - 5)° = 13×3 - 5 = 34°
The sum of seven and 5 times a number is 48
Answer:
The sum of seven and five is 12 so the number would be 4 because 12 times 4 is 48 so the answer is "4" please give me brainliest!!
Name 2 alternate exterior angles
Answer: Alternate exterior angles are formed by a transversal intersecting two parallel lines . They are located "outside" the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate exterior angles.
Step-by-step explanation:
ABCD is rotated counterclockwise about the origin. By how many degrees
was ABCD rotated?
5. List the vertices and find the eccentricity of the ellipse: (x + 1)2 + (y – 2)2 = 1
36 100
Answer:
x+y= 136099
&'&**!;;#$*$*$$-%-%=-$*$&2=28%%"
f (x) = 2x + 1, then f-1 (2) =
(x+1)
12
True
False
Answer:
False
Step-by-step explanation:
100 L 99 mL + 2,999 mL = __________________ mL
#12 Eva took out a 5-year loan to buy a car at a 2% simple interest rate. If she has to pay $1,200 in interest, how much principal did she borrow? *
Answer:
$12,000
Step-by-step explanation:
2% for 5 years is 10% in total. if after the 5 years she gotta pay 1200, this mean 0.1p=1200
multiply 10 on both sides to find p, or principal.
p=12000
Answer:
$12,000
Step-by-step explanation:
P = 1200 / ( 0.02 × 5 ) = 12000
P = $ 12,000.00
A recipe for banana bread requires 3 cups of bananas for every 1 1/2 cups of sugar used. At this rate, how many cups of sugar should be used if 8 cups of bananas are used?
Answer:
12
Step-by-step explanation:
3=1 1/2
3/8 = 1.5/x
So you cross multiply
3x + (8 x 1.5)
So 12 would be your answer.
Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it uses different media to reach potential buyers. The mean annual family income for 15 people making inquiries at the first development is $150,000, with a standard deviation of $40,000. A corresponding sample of 25 people at the second development had a mean of $180,000, with a standard deviation of $30,000. Assume the population standard deviations are the same.
1. State the decision rule for 0.05 significance level: H0: μ1 = μ2; H1:μ1 ≠ μ2.2. Compute the value of the test statistic
Answer:
The decision rule is
Reject the null hypothesis
The test statistics is [tex]t = -2.699[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 15[/tex]
The mean at first deployment is [tex]\= x _1 = \$ 150 000[/tex]
The standard deviation is [tex]s_1 = \$ 40000[/tex]
The second sample size is [tex]n_2 = 25[/tex]
The mean at second deployment is [tex]\= x_2 = \$ 180000[/tex]
The standard deviation is [tex]s_2 = \$ 30 000[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 \ne \mu_2[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df =n_1 + n_2 -2[/tex]
=> [tex]df =40 -2[/tex]
=> [tex]df =38[/tex]
Generally the pooled variance is mathematically represented as
[tex]s_p^2 = \frac{x(n_1 -1) s_1^2 + (n_2 - 1)s_2^2}{df}[/tex]
=> [tex]s_p^2 = \frac{(15 -1) 40000^2 + (25 - 1)30000^2}{38}[/tex]
=> [tex]s_p^2 = 1.1579 * 10^{9}[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x_1 - \= x_2 }{\sqrt{s_p [\frac{1}{n_1} + \frac{1}{n_2} ]} }[/tex]
=> [tex]t = \frac{ 150000 - 180000 }{\sqrt{1.11579 *10^{9} [\frac{1}{15} + \frac{1}{25} ]} }[/tex]
=> [tex]t = -2.699[/tex]
Generally from the t distribution table the probability corresponding to the t statistics value to the left is
[tex]t_{-2.699 , 38} = 0.00516046[/tex]
Generally the p -value is mathematically represented as
[tex]p-value = 2* t_{-2.699, 38}[/tex]
=> [tex]p-value = 2* 0.00516046[/tex]
=> [tex]p-value = 0.01032[/tex]
From the obtained value we see that the [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
Graph the function f(x) = x^3+2x^2-3
In one month Kimberly earned $500 at her part-time job, and $50 was withheld for federal income tax. Suppose she earns $750 next month. How much will be withheld for federal income
Answer:
It will be withheld $75 for federal income.
Step-by-step explanation:
Proportions
Assuming the federal income tax is proportional to the earnings, we can establish the following relationship between the income tax (T) and the earnings (E):
T = k.E
Kimberly earned E=$500 and paid T=$50 for federal income tax, With this information, we can calculate the value of k:
50 = k ( 500)
k = 50 / 500
k = 0.1
The model is now:
T = 0.1*E
If Kimberl earns $750 next month, the tax will be:
T = 0.1*($750)
T = $75
It will be withheld $75 for federal income.
Gary got on the Ferris wheel at the amusement park at 2:40 P.M. It went around many times and finally let him off at 3:16 P.M. How long was Gary on the ride?
Answer:
2:40 to 3:16
2:40 to 3 is 20 min
3 to 3:16 is 16 min
20+16=36
So, Gary was on the ride for 36 minutes!
