Answer:
1 real root 2 imaginary roots
Step-by-step explanation:
f(x) = x^3 + 5x^2 + x + 5
Set equal to zero to find the zeros
0 = x^3 + 5x^2 + x + 5
Factor by grouping
0 = x^2( x+5) + 1( x+5)
0 = (x+5) ( x^2+1)
Using the zero product property
x+5 =0 x^2+1 =0
x=-5 x^2 = -1
x=-5 x = ±i
1 real root 2 imaginary roots
Answer:
1 real root 2 imaginary roots
Step-by-step explanation:
f(x) = x^3 + 5x^2 + x + 5
Set equal to zero to find the zeros
0 = x^3 + 5x^2 + x + 5
Factor by grouping
0 = x^2( x+5) + 1( x+5)
0 = (x+5) ( x^2+1)
Using the zero product property
x+5 =0 x^2+1 =0
x=-5 x^2 = -1
x=-5 x = ±i
1 real root 2 imaginary roots
Refer to the figure. Which Theorem guarantees L and M are parallel
Answer:
alternate exterior angles converse
1/3÷7 3/4 dividing fraction
Answer:
4/93 or 0.04301075...
Step-by-step explanation:
Reduce the expression by cancelling the common factors
The midpoint of segment AB is (4,2). If the coordinates of A are (6,-4) what are the coordinates of B
Answer:
(2, 8)
Step-by-step explanation:
The midpoint of a line segment is calculated by taking the average of the x and y coordinates.
(2, 8) is the coordinates of b, because the midpoint is ( (6+2)/2, (-4+8)/2) ,which is (4,2).
Hope this helped, and if it did, please consider giving me a brainliest. (:
What expression is 8/12 eual to?
Answer:
8/12 = 2/3
Step-by-step explanation:
What is the correct fraction and decimal form of 10-4?
Answer:
0.0001
Step-by-step explanation:
10^-4 = 0.0001
3. A new process has been developed for applying pho toresist to 125-mm silicon wafers used in manufac turing integrated circuits. Ten wafers were tested, and the following photoresist thickness measurements (in angstroms x 1,000) were observed: 13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002. a. Test the hypothesis that mean thickness is 13.4 x 1,000 A. Use a = 0.05 and assume a two-sided alternative. b. Find a 99% two-sided confidence interval on mean photoresist thickness. Assume that thickness is normally distributed.
Answer:
a
The null hypothesis is [tex]H_o : \mu = 13.4000[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 13.4000[/tex]
The null hypothesis is rejected
b
The 99% confidence level is [tex]13.3930 < \mu < 13.3994 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 10
The population mean is [tex]\mu = 13.4 000 \ angstroms[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The sample data is
13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{13.3987+ 13.3957\cdots +13.4002 }{10}[/tex]
=> [tex]\= x = 13.3962 [/tex]
Generally the sample standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 + (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2 }{10} }[/tex]
=> [tex]\sigma =0.0039 [/tex]
The null hypothesis is [tex]H_o : \mu = 13.4000[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 13.4000[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{13.3962 - 13.4000}{\frac{0.0039}{\sqrt{10} } }[/tex]
=> [tex]z = 3.08[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2P( z > 3.08)[/tex]
From the z-table [tex]P(z > 3.08)= 0.001035[/tex]
So
[tex]p-value = 2* 0.001035[/tex]
[tex]p-value = 0.00207[/tex]
So from the obtained value we see that
[tex]p-value < \alpha[/tex]
Hence the null hypothesis is rejected
Consider the b question
Given that the confidence level is 99% then the level of significance is
[tex]\alpha = (100 -99)\%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{0.0039}{\sqrt{10} }[/tex]
=> [tex]E = 0.00318[/tex]
Generally the 99% confidence interval is mathematically represented as
[tex]13.3962 - 0.00318 < \mu < 13.3962 + 0.00318 [/tex]
=> [tex]13.3930 < \mu < 13.3994 [/tex]
Find two consecutive whole numbers that 10 lies between
Answer:
3<√10<4Step-by-step explanation:
Hope this helps0.315 ___ 0.615 what sign do i put
Answer:
Less than - hope it helpssssss
Step-by-step explanation:
Question 5 of 8 -
Eureka Math G5 EOMI Assessment (2020-2021)
Which choice is a reasonable product for the expression 8 x 2.48 ?
O 1.984
19.84
198.4
0 1984
Explain why your choice is correct using words and numbers.
Answer:
8 x 2.48 = 19.84
Step-by-step explanation:
We need to find the product for the expression 8 x 2.48.
First no is 8 and second no is 2.48
Product means to multiply.
We can write 2.48 as [tex]\dfrac{248}{100}[/tex]
i.e.
[tex]8\times \dfrac{248}{100}\\\\=\dfrac{1984}{100}[/tex]
Now, apply decimal after 9. So,
8 x 2.48 = 19.84
Hence, the correct option is (b).
A clylinder has a height of 12 centimeters and a radius of 19 centimeters. What is its volume?
13602. 48 cm³
Step-by-step explanation:Hi there !
Cylinder volume formula
V = π·r²·h
π ≈ 3.14
replace
V = 3.14×(19cm)²×12cm
= 3.14×361cm²×12cm
= 13602. 48 cm³
Good luck !
4. How many ones is in the number 500? *
(10 Points)
500 ones
50 ones
5 ones
Answer:
500 ones hope this helps
Sally started with $100 and is saving for a new Uggs. The first month she had $124, the next month $148, and by the third month she had $172 saved. Write an explicit rule to represent how much she saves each month.
An = 100n + 24
An = 24n + 124
An = 124n + 24
An = 24n + 100
Find the first of three consecutive even integers if the sum of the first and second is 15 less than 3 times the third.
Answer:
First even integer: 6
Step-by-step explanation:
Inequalities
Assume x is the first even integer. The next integer is x+2, and the last integer ix x+4.
The condition states that the sum of the first and the second number is 15 less than three times the third. This takes us to the inequality:
[tex]x+x+2<3(x+4)-15[/tex]
Operating:
[tex]2x+2<3x+12-15[/tex]
Subtracting 2 and 2x:
[tex]0<3x+12-15-2x-2[/tex]
Simplifying:
[tex]0<x-5[/tex]
Solving:
x>5
There are infinitely many solutions. For example, for x=6 (first even number into the solution interval):
First integer: 6
Second integer: 8
Third integer: 10
There are other solutions, like 20,22,24 but the first set is 6,8,10.
if a polygon is a triangle, then it has exactly three sides. is the converse of the conditional true?
Answer:
If a polygon is a triangle then it has exactly three sides
A polygon has 3 sides if and only if it is a triangle. Put it all together: Conditional: If a polygon is a triangle, then it has three sides. Converse: If a polygon has three sides, then it is a triangle.
Answer:
yes
Step-by-step explanation:
because the polygon it has tree sides it's called triangle hope it's helpThe sum of a twice a number and three is 15. What is the number?
Answer:
The answer is 6. Does that help?
Please help!!! How do I go about solving the cardinality of the Venn Diagram shown below?
A 10-foot ladder is placed 4 feet from the edge of a building. How far up the building does the ladder reach. Round your answer to the nearest tenth of a foot.
HELP ME, ILL GIVE YOU ALOT OF POINTS!! AND BRAINY AWARD!!
Answer:
a = 9.2
Step-by-step explanation:
a^2+4^2= 10^2
a^2 + 16 = 100
a^2 = 84
a = 9.2
HELP What is the slope of the line that contains points (-6, -6) and (-3, 1)?
In Vladivostock, Siberia, the noon temperature was 13°C, but then it dropped to –31°C by midnight. What was change in temperature? (Be sure to include your expression
Answer:
there was a 44 degree change in the tenpature
Which of the following equations is equivalent to 4(6p – 3) = 26?
A: 10p – 1 = 26
B:24p – 12 = 26
C: 10p – 7 = 26
D: 24p – 3 = 26
Answer:
B. 24p - 12 = 26
For both 4(6p – 3) = 26 and 24p - 12 = 26, [tex]p = \frac{19}{12}[/tex]
I hope that this helps you!
Answer:
B:24p – 12 = 26
Step-by-step explanation:
(2t - 4)(3t + 3)
Find the product. Simplify for answer
✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽
[tex](2t-4)(3t+3)[/tex]
[tex]= (2t + -4) (3t + 3)[/tex]
[tex]= (2t) (3t) + (2t) (3) + (-4) (3t) + (-4) (3)[/tex]
[tex]= 6t^2 + 6t - 12t - 12[/tex]
[tex]= 6t^2 - 6t - 12[/tex]
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ May ♡
Find the perimeter of the following polygon. Be sure to include the correct unit in your answer.
15 m
1
mm
15 m
17 m
km
9 m
12 m
Answer:
489 km is the perimeter
Step-by-step explanation:
mark me BRAINLIEST
Dante rode his bike a mile in 5 minutes. At that rate, how many miles can he ride in an hour?
Answer:
Step-by-step explanation:
direct proportion
1mile in 5 minutes
xmiles in 60 minutes
cross multiply
60/5=12 miles
Answer:
12 miles
Step-by-step explanation:
1×12=12 a clock has 60 minutes per hour 60÷5=12 12×1=12
Which of the following shows the equation solved for y?
2x + 6y = -12
Answer:
Here it goes -0.333
A fish tank holds 175 gallons of water. Tom is emptying the tank and
removes 25 gallons per hour. Write an equation to model the situation,
where x represents time in hours and y represents the number of gallons
of water in the fish tank.
Gavin bought 6.5 dozen carnations. He spent $68.25 on the flowers. How much did each flower cost?
First, find the total number of flowers by 6.5 by 12.
The total number of flowers is .
Then $68.25 by the total number of flowers to find the cost of each flower.
Each flower will cost approximately .
Please help! 75 points!
Answer:
$0.84
Step-by-step explanation:
6.5 x 12 = 78 total # of flowers
or 68.25 divided by .875= 78.
≈$0.84 approximately
Answer:
Gavin bought 6.5 dozen carnations. He spent $68.25 on the flowers. How much did each flower cost?
First, find the total number of flowers by
✔ multiplying
6.5 by 12.
The total number of flowers is
✔ 78
.
Then
✔ divide
$68.25 by the total number of flowers to find the cost of each flower.
Each flower will cost approximately
✔ $0.90
.
Step-by-step explanation:
I got this question wrong for you to see the answer
Slope : 3/1 through (3,-1)
Answer: y=1/3x or y−1=1/3(x−3)
Step-by-step explanation:
27=p(1+r3) solve for r
p = 27
r = 0
p(1+r3) = 27
27(1+0(3)) = 27
27(1+0) = 27
27(1) = 27
27 = 27
Eric earns $7.50 per hour working at a grocery store. The total amount of money he
earns on a given day is a function of how many hours he works that day?
Answer: 37.50
Step-by-step explanation: If he works 5 hours A DAY and he earns $7.50 PER HOURS, you just need to multiple
7.50(5)= 37.50
HELP!!!! Additive Identify property stuff!!!!
Answer:
i am pretty sure it is F
Step-by-step explanation:
Answer:f?
Step-by-step explanation: