Done
[tex] \pink{\underline{\boxed{8a²+a-7}}}[/tex]
Solution :-
[tex]\Longrightarrow\sf{(3a ^2 + 2a) + (5a^2 -a-7)}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{3a^2+ 2a + 5a^2-a-7}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{8a^2+2a-a-7}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \Longrightarrow\sf{8a^2+1a-7}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{8a^2+a-7}[/tex]
[tex]\red{━━━━━━━━━━━━━━━━━━━━━━}[/tex]
4.5,4.316,4.32,4.312 from least to greatest
4.5, 4.316, 4.32, 4.312
= 4.500, 4.316, 4.320, 4.312
Look at the thousandths and hundreths place in the decimal section.
Least to greatest = 4.312 < 4.316 < 4.32 < 4.5
Based on a sample of 20 people, the sample mean GPA was 3.25 with a standard deviation of 0.02
The test statistic is:
(to 2 decimals)
The critical value is:
(to 2 decimals)
Using the t-distribution, it is found that:
The test statistic is t = -11.18.The critical value is [tex]t^{\ast} = \pm 2.093[/tex].What are the hypotheses tested?At the null hypothesis, it is tested if the mean GPA of the students is of 3.3, that is:
[tex]H_0: \mu = 3.3[/tex]
At the alternative hypothesis, it is tested if the mean GPA is different than 3.3, hence:
[tex]H_1: \mu \neq 3.3[/tex].
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 3.25, \mu = 3.3, s = 0.02, n = 20[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{3.25 - 3.3}{\frac{0.02}{\sqrt{20}}}[/tex]
t = -11.18.
We are testing if the mean is different of a value, hence we have a two-tailed test, with 20 - 1 = 19 df and a standard significance level of 0.05, hence, using a t-distribution calculator, the critical value is [tex]t^{\ast} = \pm 2.093[/tex].
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Select the expression that represents the following statement: multiply the difference of 5 and 2 by 7, and then add 6. 7 x (5 − 2) + 6
5 + 2 x 7 + 6
7 x (5 + 2) − 6
6 − 2 + (7 x 5)
Answer:
7(5-2)+6
Step-by-step explanation:
difference - subtraction
putting the 7 next to it means that it will multiply times that first
Can you please Find x I’m trying to finish before school ends
Answer:
-7.35
Step-by-step explanation:
7/x = cos(60)
x = 7(cos(60))
x = 7/(-0.95)
x = -7.35
Justine bought a pair of boots for $76.68 and paid 13% sales tax. What was the price of these boots including tax?
Answer: $86.65
Step-by-step explanation:
First, find how much Justine paid in tax. To do this, first convert 13% to a decimal by dividing by 100. This gets a tax rate of 0.13. Now, multiply the price of the boots by the tax rate. 76.68*0.13 = 9.9684. Round to the nearest cent to get $9.97.
Now, add the amount paid in tax to the price of the boots. 76.68+9.97 = $86.65.
A car rental company charges $120 plus $0.37 per mile, m. Which equation represents the total cost, c, of renting a car?
Simplify 22-2(12/4+2*3)/3+7
Answer: 23
Step-by-step explanation:
A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 .
Sheriff Aniskin receives confidential information: the thief with the stolen accordion
has been traveling on a raft for 2 hour 40 minutes from Village Ivanovo toward
Village Sosnovka. Aniskin immediately leaves Sosnovka in a motorboat and travels
upstream toward the raft. Aniskin catches the thief 27 km from Sosnovka. Find the
speed of the raft if the speed of the motorboat in still water is 12 km/h and the
distance from Ivanovo to Sosnovka is 44 km.
The speed of the raft if the speed of the motorboat in still water is 3 km/h
What is speed?
Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Let the speed of the raft (current) - r
Speed of motorboat - 12 km/h
The distance between villages - is 44 km
Let the time spent by Aniskin - t
The time the thief was in travel = 2 hr 40 min + t = 2 40/60 + t = 3/8 + t
The distance the thief traveled = 44 - 27 = 17 km
We have the following equations:
r(8/3 + t) = 17
(12 - r)t = 27
Simplify the equations:
r(8/3 + t) = 17 ⇒ rt + 8/3r = 17
(12 - r)t = 27 ⇒ 12t - rt = 27
Add up the equations and solve for r:
rt + 8/3r + 12t - rt = 44
8/3r + 12t = 44
r = 16.5 - 4.5t
Substitute r into the second equation:
(12 - 16.5 + 4.5t)t = 27
4.5t² - 4.5t = 27
9t² - 9t - 54 = 0
Solving we get
t = 3 h
Find r:
r = 16.5 - 4.5*3 = 3 km/h
Therefore the speed of the raft if the speed of the motorboat in still water is 3 km/h
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convert 32 table spoons to cup
Answer:
2 cups
Step-by-step explanation:
Formula: divide the volume value by 16
so its 32 divided by 16
The probability that an international flight leaving the United States is delayed in departure in (event D) is .27. The probability of an international flight leaving the United States is a transpacific flight (event P) is .58. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .14.
(Q) What is the probability that an international flight leaving the United States is delayed given that the flight is a trnaspacific flight?
The probability that an international flight leaving the United States is delayed given that the flight is a trnaspacific flight is 0.241
How to determine the probability?The given parameters are:
P(D) = 0.27
P(P) =0.58
P(D and P) = 0.14
The required probability is then calculated using:
P(D | P) = P(D and P)/P(P)
This gives
P(D | P) = 0.14/0.58
Evaluate
P(D | P) = 0241
Hence, the required probability is 0.241
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Solve for xxx.
Enter the solutions from least to greatest.
(-5x +4)(x -3)=0(−5x+4)(x−3)=0left parenthesis, minus, 5, x, plus, 4, right parenthesis, left parenthesis, x, minus, 3, right parenthesis, equals, 0
\text{lesser }x =lesser x=start text, l, e, s, s, e, r, space, end text, x, equals
\text{greater } x =greater x=start text, g, r, e, a, t, e, r, space, end text, x, equals
Then the two solutions of the quadratic equation are 4/5 and 3.
How to solve the equation?
Here we want to solve the quadratic equation:
(-5x + 4)*(x - 3) = 0
The two solutions are the values of x for which each parenthesis becomes equal to zero, so the two solutions are given by:
-5x + 4 = 0
x - 3 = 0
If we solve these two equations we get:
x = -4/-5 = 4/5
x = 3
Then the two solutions are 4/5 and 3.
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the camera cost $540 if the sales tax is 7.2% what is the tax change and the total cost?
Answer:
38.88
Step-by-step explanation:
Convert the problem to an equation using the percentage formula: P% * X = Y.
P is 10%, X is 150, so the equation is 10% * 150 = Y.
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
Becky bought a display case with a rectangular lid that is 134 feet long and 56 feet wide.
What is the area of the lid?
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
ft²
Answer:
1 11/24
Step-by-step explanation:
u multiply both numeators and both denominators for example 1 3/4 5/6 i would first turn 1 3/4 into 7/4 and then multiply
The ratio of cats to dogs at pet shelter is 4 to 3. if there are 36 dogs, how many cats are there?
A. 27
B. 36
C. 48
D. 52
Holly scored an 88, 91, 89, 84, and a 98 on the last five math tests. What is her mean test score?
Answer:the mean is 90
Step-by-step
you find the sum of the values then divide them by the amount of numbers in the set
find the center and the radius of the circle (x-7)^2+(y+4)^2=81
A circle is a curve sketched out by a point moving in a plane. For the given equation of a circle, the centre will lie at the coordinate (7,-4), while the radius will be equal to 9 units.
What is the equation of the circle with radius r units, centred at (x,y)?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
If a circle O has a radius of r units length and it has got its centre positioned at (h, k) point of the coordinate plane, then, its equation is given as:
(x-h)² + (y-k)² = r²
Given the equation of the circle is (x-7)²+(y+4)²=81. The equation can be rewritten as,
(x-7)² + [y-(-4)]² = 9²
Hence, For the given equation of a circle, the centre will lie at the coordinate (7,-4), while the radius will be equal to 9 units.
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You flip a coin and then roll a 6-sided number cube (a die).
a. When finding the probability, does it matter whether you roll the die or flip the coin first?
b. Is there more than one way to draw a tree diagram for this problem? If so, does that change the likelihood that any outcome will occur?
c. Draw the shape of the tree diagram that you would use.
d. How many outcomes are there? List them.
e. Find the probability of rolling an even number and getting heads.
Answer:
a) No, it does not matter whether you roll the die or flip the coin first, as these two events are independent of each other, which means they do not affect each other.
b) Yes.
Let event 1 be flipping a coin and event 2 be rolling a die.Let event 1 be rolling a die and event 2 be flipping a coin.The likelihood that any outcome will occur will not change, as the events are independent.
c) see attached
d) 12 outcomes (H = head, T = tail, numbers represent the value of the die)
H 1 T 1
H 2 T 2
H 3 T 3
H 4 T 4
H 5 T 5
H 6 T 6
e)
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(even)=\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}[/tex]
[tex]\implies \sf P(head)=\dfrac{1}{2}[/tex]
[tex]\implies \sf P(even)\:and\:P(head)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}[/tex]
Help! Is my working correct/wrong? If my working is wrong, sorry to trouble you but can you pls correct it?
THANKS IN ADVANCE!!
NONSENSE = REPORT
NO ALGEBRA! PLEASE! THANKS!!!!!
Answer:
∠ e = 20°
Step-by-step explanation:
you should have also subtracted 2e from the 360
since UV is a straight line, the angles lying on it sum to 180° , that is
90° + e + 70° = 180°
e + 160° = 180° ( subtract 160° from both sides )
e = 20°
When the common ratio of an
infinite geometric sequence is
less than 1, its sum can be
found by the formula
a
where s is the sum, a is the first
term, and r is the common
ratio, What is the sum of the
geometric sequence below?
16,8,4,2.
The sum of the infinite geometric sequence 16, 8, 4, 2 is 32
How to find the sum of a geometric sequence?The sum can be represented as follows:
s∞ = a / 1 - r
where
r = common ratio
a = first term
Therefore,
r = 8 / 16 = 1 / 2
a = 16
hence,
s = 16 / 1 - 1 / 2
s = 16 / 1 / 2
s = 16 × 2 / 1
s = 32
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find the speed and direction of a plane with a velocity of 〈5,-12〉.
Answer:
Below in bold.
Step-by-step explanation:
Speed = √(5^2 + (-12)^2)
= √169
= 13,
Direction = arctan (5/-12)
= -22.61 degrees ( its in the 4th quadrant)
So we can write the direction as 90 + 22.61
= 112.61 degrees.
If
x
=
−
9
and
y
=
2
, evaluate the following expression:
2
(
y
−
3
x
y
)
jenette ordered a large bucket of popcorn at the movies.the graph shows the amount of popcorn in her bucket over time
Answer:
A
Step-by-step explanation:
They had taken 8 galons of water along the bus. If there were 62 sixth graders and 2 teachers how many cups did each person get
Answer:
2
Step-by-step explanation:
8gallons=16 cup
8x16=128
62+2=64
128÷2=64
The prisms are similar. What is the surface area of Prism B?
Prism A is 10 m. Prism B is 3 m. Surface area = 880m2
Answer:
Both of the prism are similar , Then
prism A is 10m and it's surface area is 880m²
Now,
prism B is 3m and it's surface area will be = 264m²
establish the exact displacement expression and shape functions for the given tapered axial member. Formulate the relevant stiffness matrix
The displacement is represented from the starting position to the final position.
What is displacement?Your information is incomplete. Therefore, an overview of displacement will be given. It should be noted that displacement simply means a vector whose length is the shortest distance from the initial position to the final position.
In this case, the displacement will be:
= Final position - Initial position
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Which is an equation of the line passing through (-2,3) and perpendicular to the line
5x-y=12?
Answer:
y = -1/5x + 2.6
Step-by-step explanation:
Put the equation into slope intercept form:
5x - y = 12
-y = -5x + 12
y = 5x - 12
The slope of a perpendicular line will be the opposite reciprocal.
So, the slope of the new line will be -1/5
Then, plug this slope and the given point into the equation y = mx + b to find b
y = mx + b
3 = -1/5(-2) + b
3 = 0.4 + b
2.6 = b
So, the equation will be y = -1/5x + 2.6
Solve for x.
Your answer must be simplified
15<−5x
Graph the equations to find the solution(s) to the system. y=x+3y=13(x+5)(x−1) Use the Line tool to graph the line. Use the Parabola tool to graph the parabola. Choose maximum or minimum point first and then a point on the parabola.
The solutions to the equations are (1.702,4.7) and (-4.7,-1.7).
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The two given equations ( x + 3 ) and ( 13 ( x+5)(x-1) intersects at the ponits (1.702,4.7) and (-4.7,-1.7).
The graph of the above equations is attached with an answer.
Therefore the solutions to the equations are (1.702,4.7) and (-4.7,-1.7).
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Please help! I forgot to study..
Answer:
mean: $13.50
median: $11
mode: $10
range: $26
hope this helps:)
Answer:
The mean is 13.5, median is 11, mode is 10, and for the range, it's 26
Step-by-step explanation:
For the mean, you add all the numbers up 4+30+10+12+10+20+12+10 = 108. Then you divide by how many terms there are which is 8 and then you get 13.5.
The median is the middle value in a list ordered from smallest to largest. So that is why you get 11.
The mode is the most frequently occurring value on the list and we can tell that 10 is the most occuring in this list.
Finally we have the range. To find the range you subtract the highest amount to the lowest amount. 30 - 4 = 26.
Complete the table above. Also, find the number students that can be chaperoned by 9 teachers.
