Answer:
[tex]\boxed{2y^{2} - y - 15}[/tex]
Step-by-step explanation:
Use the FOIL technique in order to distribute the terms properly. FOIL stands for First Terms, Outside Terms, Inside Terms, and Last Terms. In order to properly distribute, multiply the common terms based on the steps in the FOIL technique. So, in this case:
The first terms are 2y and y. The outside terms are 2y and -3. The inside terms are 5 and y.The last terms are 5 and -3.Therefore, multiply the terms:
2y and y to get 2y²2y and -3 to get -6y5 and y to get 5y5 and -3 to get -15Then, add or subtract based on the signs:
2y² - 6y + 5y - 15
Then, add like terms to finish simplifying the expression. This leaves you with 2y² - y - 15.
Answer:
2y2 – y – 15
Step-by-step explanation:
(2y + 5)(y – 3)
= 2y(y – 3) + 5(y – 3)
= 2y2 – 6y + 5y – 15
= 2y2 – y –15
if y = 2√x÷ 1–x', show that dy÷dx = x+1 ÷ √x(1–x)²
Answer: see proof below
Step-by-step explanation:
Use the Quotient rule for derivatives:
[tex]\text{If}\ y=\dfrac{a}{b}\quad \text{then}\ y'=\dfrac{a'b-ab'}{b^2}[/tex]
Given: [tex]y=\dfrac{2\sqrtx}{1-x}[/tex]
[tex]\sqrtx[/tex][tex]a=2\sqrt x\qquad \rightarrow \qquad a'=\dfrac{1}{\sqrt x}\\\\b=1-x\qquad \rightarrow \qquad b'=-1[/tex]
[tex]y'=\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)}{(1-x)^2}\\\\\\.\quad =\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)\bigg(\dfrac{\sqrt x}{\sqrt x}\bigg)}{(1-x)^2}\\\\\\.\quad =\dfrac{1-x+2x}{\sqrt x(1-x)^2}\\\\\\.\quad =\dfrac{x+1}{\sqrt x(1-x)^2}[/tex]
LHS = RHS: [tex]\dfrac{x+1}{\sqrt x(1-x)^2}=\dfrac{x+1}{\sqrt x(1-x)^2}\qquad \checkmark[/tex]
in a gp the sixth term is 8 times the third term, and the sum of the seventh and eighth term is 192. determine the common ratio
Answer:
common ratio = 2
Step-by-step explanation:
T6 = ar^5
T3 = ar²
T6 = 8 x T³
ar^5 = 8 x ar²
ar^5/ar² = 8
r³ = 8
r = ³√8
r = 2
Find the value of the test statistic z using . The claim is that the proportion of adults who smoked a cigarette in the past week is less than , and the sample statistics include n subjects with saying that they smoked a cigarette in the past week.
Correct question is;
The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.35, and the sample statistics include n = 1168 subjects with 385 saying that they smoked a cigarette in the past week. Find the value of the test statistic
Answer:
Test statistic is z = -1.46
Step-by-step explanation:
Let's first of all define the hypotheses:
Null hypothesis:
H0: p = 0.35, i.e 35% in the sample of 1,168 adults have smoked cigarettes in the previous week.
Alternative hypothesis:
Ha: p < 0.35, i.e less than 35% in the sample of 1,168 adults have smoked cigarette in the previous week.
The sample size is, n = 1,168 while the number of adults who smoked in the previous week would be; x = 385
Therefore, the sample proportion of adults who smoked in the previous week would be calculated as;
p^ = x/n = 385/1168 ≈ 0.3296
Now, from Central Limit Theorem for large samples, The sampling distribution of the sample proportion p^, will have a mean of μ = p = 0.35
Formula for standard deviation is;
σ = √[p (1 – p)/n]
σ = √(0.35 × (1 – 0.35)/1168)
σ = √0.0001947774
σ = 0.014
Formula for test statistic is;
z = (p^ - p)/σ
z = (0.3296 - 0.35)/0.014
z = - 1.46
The length and width of a rectangle are measured as 58 cm and 45 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
Error in calculated area = [tex]\pm 10.3 cm^2[/tex]
Step-by-step explanation:
x = 58 cm
y = 45 cm
A = x*y
delta A
= delta (x*y)
= y delta x + x delta y (neglecting small qty delta x * delta y = 0.01)
= 45(0.1) + 58(0.1)
= 103(0.1)
= 10.3 cm^2
A right circular cone has a volume of 30π m. If the height of the cone is multiplied by 6 but the radius remains fixed, which expression represents the resulting volume of the larger cone?
A. 6 + 30π m
B. 6 x 30π m
C. 6 x 30π m
D. 6 x (30π) m
PLZ HURRY IM TIMED
Answer:
Below
Step-by-step explanation:
The formula of the volule of a cone is:
● V= (1/3) × Pi × r^2 × h
h is the height and r is the radius.
■■■■■■■■■■■■■■■■■■■■■■■■■■
We are given that the volume is 30 Pi m^3
● V = 30 Pi
● 1/3 × Pi × r^2 × h = 30 Pi
If we multiply h by 6 we should do the same for 30 Pi since it's an equation
● 1/3 × Pi × r^2 × h = 30 × Pi × 6
Answer:
REVIEW: B is Correct Exit
A right circular cone has a volume of 30π m. If the height of the cone is multiplied by 6 but the radius remains fixed, which expression represents the resulting volume of the larger cone?
A. 6 + 30π m
B. 6 x 30π m
C. 6 x 30π m
D. 6 x (30π) m
Step-by-step explanation:
The answer is be all i did was dig into what the other person was saying and got b it is correct:)
. Simplify the sum. (2u3 + 6u2 + 2) + (7u3 – 7u + 4)
Answer:
9u^3 + 6u^2 - 7u + 6
Step-by-step explanation:
I need help with this question.
Answer:
Complement = 15 Degrees
Supplement = 105 Degrees
Step-by-step explanation:
The complement of an angle refers to the measure that will make the angle 90 degrees. So, the complement of 75 would be 15, since 90 - 75 = 15.
The supplement of an angle refers to the measure that will make the angle 180 degrees. So, the supplement of 75 would be 105, since 180-75 = 105.
Cheers.
T= 2pi times the sqrt of l/g (l=2.0m; g= 10m/s^2
Answer:
v (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?
Step-by-sv (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?tep explanation:
What is the solution to this system of linear equations?
y-x = 6
y + x = -10
(-2,-8)
(-8.-2)
(6.-10)
(-10.6)
Answer:
The correct answer is A
Step-by-step explanation:
Answer:
(-8, -2)
Step-by-step explanation:
y-x = 6
y + x = -10
Add the two equations together to eliminate x
y-x = 6
y + x = -10
--------------------
2y = -4
Divide by 2
2y/2 = -4/2
y = -2
Now find x
y+x = -10
-2+x = -10
x = -8
the height of a triangle is 2 centimetres more than the base. if the height is increased by 2 centimetres while the base remains the same, the new area becomes 82.5 centimetres square. find the base and the height of the original triangle.
Answer:
Base = 11 cm
Height = 13 cm
Step-by-step explanation:
It is given that the height of a triangle is 2 centimetres more than the base.
Let x cm be the base of triangle. So height of the triangle is x+2 cm.
It is given that if the height is increased by 2 centimetres while the base remains the same, the new area becomes 82.5 centimetres square.
New height = (x+2)+2 = x+4 cm
Area of a triangle is
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
[tex]82.5=\dfrac{1}{2}\times x\times (x+4)[/tex]
[tex]165=x^2+4x[/tex]
[tex]x^2+4x-165=0[/tex]
Splitting the middle term, we get
[tex]x^2+15x-11x-165=0[/tex]
[tex]x(x+15)-11(x+15)=0[/tex]
[tex](x+15)(x-11)=0[/tex]
Using zero product property, we get
[tex]x=-15,11[/tex]
Base of a triangle can not be negative, therefore x=11.
Base = 11 cm
Height = 11+2 = 13 cm
Therefore, the base of original triangle is 11 cm and height is 13 cm.
Evaluate x^2 − 4x + 5, when x = − 3
Answer:
[tex]\huge\boxed{26}[/tex]
Step-by-step explanation:
[tex]\sf x^2-4x+5\\Given \ that \ x = -3\\(-3)^2-4(-3)+5\\9+12+5\\26[/tex]
Answer:
[tex] \boxed{26}[/tex]
Step-by-step explanation:
[tex] \mathsf{ {x}^{2} - 4x + 5}[/tex]
[tex] \mathrm{Plug \: the \: value \: of \: x}[/tex]
⇒[tex] {( - 3)}^{2} - 4 \times(- 3 )+ 5[/tex]
[tex] \mathrm{Evaluate \: the \: power}[/tex]
⇒[tex] \mathsf{9 - 4 \times(- 3 ) + 5}[/tex]
[tex] \mathrm{Multiply \: the \: numbers}[/tex]
⇒[tex] \mathsf{9 + 12 + 5}[/tex]
[tex] \mathrm{Add the numbers}[/tex]
⇒[tex] \mathsf{26}[/tex]
Hope I helped!
Best regards!
Define “constant value”
A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.
Rob sent an email survey to 2,000 cell phone owners asking about their satisfaction with their current plan. Only 256 people returned the survey and they were predominately 18-24 years old.
Which of the following statements is true?
Rob is ignoring the assumption that all survey participants will want to act independently.
The survey likely has bias because the people who could not answer differ from those who did answer.
Rob included too many people on the survey list, affecting the data collected.
The survey suffers from census issues because only 256 people responded.
Answer:
option B
everyone has different opinions about different things, since we only recorded the survey of a fourth of the total people, the survey will definitely have bias since the people who dont have to answer survey will not be able to record their opinions
in the diagram, POS,QOT and ROU are straight lines. find the value of x.
==========================================
Explanation:
Angle UOT is vertical to the angle x. This angle combines with 4x and 40 to get a straight angle of 180 degrees
(angle POU) + (angle UOT) + (angle TOS) = 180
4x + x + 40 = 180
5x + 40 = 180
5x = 180-40
5x = 140
x = 140/5
x = 28
Side note: if x = 28, then 4x = 4*28 = 112.
We see that 112+28+40 = 180, which is the sum of the three angles mentioned earlier. Since we got 180, this confirms the answer.
Allison bought jelly beans to share with her friends. She bought pounds of blueberry jelly beans and pounds of lemon jelly beans. If she gave pounds of jelly beans away to her friends, how many pounds of jelly beans does Allison have left?
Answer: [tex]1\dfrac{11}{12}\text{ pounds}[/tex]
Step-by-step explanation:
The complete question is provided in the attachment.
Given, Amount blueberry jelly beans= [tex]1\dfrac{1}{4}[/tex] pounds
[tex]=\dfrac{5}{4}[/tex] pounds.
Amount lemon jelly beans = [tex]2\dfrac{1}{3}[/tex]pounds
[tex]=\dfrac{7}{2}[/tex] pounds
Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans
[tex]=(\dfrac{5}{4}+\dfrac{7}{3})[/tex] pounds
[tex]=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}[/tex]
Amount of jelly beans she gave away = [tex]1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}[/tex]
Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away
=[tex]\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}[/tex]
She has left [tex]1\dfrac{11}{12}\text{ pounds}[/tex] of jelly beans.
Last year, Leila had $30,000 to invest. She invested some of it in an account that paid 6% simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of $1580 in interest. How much did she invest in each account?
Answer:
6%: $8,0005%: $22,000Step-by-step explanation:
Let x represent the amount invested at 6%. Then 30000-x is the amount invested at 5%. Leila's total earnings for the year are ...
0.06x +0.05(30000-x) = 1580
0.01x +1500 = 1580 . . . . . . . . . . . . simplify
0.01x = 80 . . . . . . . . . . . subtract 1500
x = 8000 . . . . . . . . . . . . multiply by 100
Leila invested $8000 at 6% and $22000 at 5%.
If “n” is a positive integer divisible by 3 and n is less than or equal to 44, then what is the highest possible value of n?
Answer:
Step-by-step explanation:
positive integer divisible by 3 includes
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...
less than highest possible value is 42
What number is equivalent to 9 1/2?
Answer:
the answer is going to be 2/4
Can u pls help I don’t understand I’ll give u 15 points
Answer: [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
This is a multiplication problem. You are multiplying [tex]\frac{1}{3}[/tex] by 4. This also means 4 divided by 3. They are both the same.
if (ax+b)(x-3) = 4x^2+cx-9 for all values of x, what is the value of c? a) -9 b) -6 c) 6 d) 9
Answer:
c=-9
Step-by-step explanation:
Hello,
[tex](ax+b)(x-3)=ax(x-3)+b(x-3)=ax^2-3ax+bx-3b\\\\=ax^2+(b-3a)x+(-3b) \\\\\text{And it should be equal to } 4x^2+cx-9[/tex]
We can identify the like terms so:
a = 4
b-3a = c
3b = 9 <=> b = 3
So c = 3 - 3*4 = 3-12 = -9
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A line is an undefined termi because it
Answer:
Goes on forever.
Step-by-step explanation:
Which of the following is -32(5x-7)(x+8)/-4(x+8)(5x-7) simplified? A.8/(x+8) B.8 C.4 D.4/(5x-7)
Answer:
work is shown and pictured
22 tons is equivalent to ______ kilograms.
Answer:
20000 kg
Step-by-step explanation:
Recall that 1 kg = 2.2 lb approximately. Then:
22 tons 1 kg 2000 lb
------------ * ------------ * -------------- = 20000 kg
1 2.2 lb 1 ton
Marco is investigating some of the business models of SureSpin, one of Faster Fidget's top competitors.
He has learned that they model their cost of production for one type of spinner with the function C(x) =13,450 + 1.28x, where x is the number of spinners produced. Interpret the model to complete the
statement.
Type the correct answer in each box. Use numerals instead of words. Based on the model, the fixed cost of production is $?
Answer:
$13,450
Step-by-step explanation:
The fixed cost of production is $13,450, this is because a fixed cost of production is the amount of cost that does not change with an increase or decrease in the amount of the goods or services produced. Fixed cost of production are paid by companies. It is one of the two component of the total cost of goods or services along with the variable cost.
In regard to the information given in the question, no matter how many spinners the company produces, the fixed cost will remain the same.
Assuming x is the variable cost which signifies the number of spinners produced, this literally implies that the cost to produce each spinner is $1.28 and the fixed cost which is independent of the production is $13,450.
Hence, the fixed cost of production is $13,450.
If mL DOC = 44º and m2 COB = 80°,
find the measure of the indicated arc
in circle o.
С
o
B.
mDEB = ?
Answer:
236°
Step-by-step explanation:
The circumference of a circle is 360° since <DOC is given as 44° and <COB is given as 80° and the center angles are equal to the arc it sees the the measure of arc DEB would be 360 - 44 - 80 = 236°
Ben and Cam are scuba diving. Ben is 15.8 meters below the
surface of the water. Cam is 4.2 meters above Ben. What is Cam's
position relative to the surface of the water?
=======================================================
Explanation:
Check out the diagram below.
Draw a vertical number line with 0 at the center. The positive values are above it, while the negative values are below it.
Between -15 and -16, closer to -16, plot the value -15.8 to indicate Ben's position. I have done so as the point B.
We move 4.2 units up to arrive at Cam's position
-15.8 + 4.2 = -11.6
So Cam is 11.6 meters below the surface of the water.
normal population has a mean of 63 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places): Greater than 65.
Answer:
0.2207
Step-by-step explanation:
Here, we want to find the probability that the sample mean is greater than 25.
What we use here is the z-scores statistic
Mathematically;
z-score = (x-mean)/SD/√n
From the question;
x = 65, mean = 63, SD = 13 and n = 25
Plugging these values in the z-score equation, we have
Z-score = (65-63)/13/√25 = 2/13/5 = 0.77
So the probability we want to calculate is ;
P(z > 0.77)
This can be obtained from the standard normal distribution table
Thus;
P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p
Suppose you have a bag with the following in it: 5 one dollar bills, 4 fives, 3 tens, 5 twenties, and 3 fifties. Assuming the experiment requires drawing one bill from the bag at random, complete the probability distribution for this experiment.
Required:
What is the probability of drawing 9 dollars or less in a single draw?
Answer:
(a) Probility Distribution
Outcome probability
$1 5/15 = 1/3
$5 4/15
$10 3/15 = 1/5
$20 5/15 = 1/3
(b) P($9 or less) = 3/5
Step-by-step explanation:
(a) Probility Distribution
Outcome probability
$1 5/15 = 1/3
$5 4/15
$10 3/15 = 1/5
$20 5/15 = 1/3
Any other denomination
0
(b)
ways to draw $9 or less in a single draw
P($1) = 1/3
P($5) = 4/15
P($9 or less) = P($1) + P($5) = 1/3 + 4/15 = 9/15 = 3/5
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true? A. ABCD is a parallelogram with non-perpendicular adjacent sides. B. ABCD is a trapezoid with only one pair of parallel sides. C. ABCD is a rectangle with non-congruent adjacent sides. D. ABCD is a rhombus with non-perpendicular adjacent sides.
Hey There!!
The answer to this is: A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?" Line BC is parallel to line AD because their slopes is equal i.e. (0 - 0) / (7 - 2) = (5 - 5) / (8 - 3) which gives 0 / 5 = 0 / 5 giving that 0 = 0. We check whether line AB is parallel to line CD. Slope of line AB is given by (0 - 5) / (2 - 3) = -5 / -1 = 5. Slope of line CD is given by (5 - 0) / (8 - 7) = 5 / 1 = 5 We have been able to prove that the opposite sides of the quadrilateral are parallel which means that the quadrilateral is not a trapezoid. Next we check whether the length of the sides are equal. Length of line AB is given by sqrt[(0 - 5)^2 + (2 - 3)^2] = sqrt[(-5)^2 + (-1)^2] = sqrt(25 + 1) = sqrt(26) Length of line BC is given by sqrt[(0 - 0)^2 + (7 - 2)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Length of line CD is given by sqrt[(5 - 0)^2 + (8 - 7)^2] = sqrt[5^2 + 1^2] = sqrt(25 + 1) = sqrt(26) Length of line DA is given by sqrt[(5 - 5)^2 + (8 - 3)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Thus, the length of the sides of the quadrilateral are not equal but opposite sides are equal which means that the quadrilateral is not a rhombus. Finally, we check whether adjacent lines are perpendicular. Recall the for perpendicular lines, the product of their slopes is equal to -1. Slope of line AB = 5 while slope of line BC = 0. The product of their slopes = 5 x 0 = 0 which is not -1, thus the adjacent sides of the quadrilateral are not perpendicular which means that the quadrilateral is not a rectangle. Therefore, ABCD is a parallelogram with non-perpendicular adjacent sides. Thus, For (option A).
Hope It Helped!~ ♡
ItsNobody~ ☆
Answer:
A. ABCD is a parallelogram with non-perpendicular adjacent sides.
Hope this helps!
Step-by-step explanation:
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.
Store's Card Major Credit Card
Sample size 64 49
Sample mean $140 $125
Population standard deviation $10 $8
A point estimate for the difference between the means is:________
a. 18
b. 265
c. 15
d. 2
