Answer:
Step-by-step explanation:
you need o solve 26=4+40t-16t^2
the equation becomes:
the equation becomes:-16t^2+40t+4-26=0
the equation becomes:-16t^2+40t+-22=0 or8t^2-20t+11=0
8t^2-20t+11=0, a=8 , b=-20 c=11 the discriminant =b^2-4ac=(-20)^2-4x8x11=48
t1=(20-squarootof48)/16 =13/16 =0.81 seconds t2=27/16=1.68 second I rounded my answers
The scores on a standardized test are normally distributed with a mean of 80 and standard
deviation of 5. What test score is 0.9 standard deviations above the mean?
Answer:
84.5
Step-by-step explanation:
Given :
Mean μ = 80
Standard deviation, σ = 5
Z = number of standard deviations from the mean, Z = 0.9
Teat score, x
Using the Zscore formula :
Zscore = (x - μ) / σ
Plugging in our values :
0.9 = (x - 80) / 5
Cross multiply
0.9 * 5 = x - 80
4.5 = x - 80
4.5 + 80 = x
x = 84.5
Test score = 84.5
Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year?
Answer:
Hari saves $ 10,320 in a year.
Step-by-step explanation:
Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:
100 - 80 = 20
4300 x 0.20 x 12 = X
860 x 12 = X
10320 = X
Therefore, Hari saves $ 10,320 in a year.
Which of the following is the solution set of 6x + 5 = -29? {-4}
Answer:
[tex]{ \tt{6x + 5 = - 29}} \\ { \tt{6x = - 36}} \\ { \tt{x = - 6}}[/tex]
Given the following constraints, find the maximum and minimum values for z. Constraints: 2x−y≤124x+2y≥0x+2y≤6 Optimization Equation: z=2x+5y
Answer:
Minimum = 0
Maximum = 15
Step-by-step explanation:
Given
Optimization Equation: [tex]z = 2x + 5y[/tex]
Constraints:
[tex]2x- y \le 12[/tex]
[tex]4x + 2y \ge 0[/tex]
[tex]x + 2y \le 6[/tex]
[tex]x,y\ge 0[/tex]
Required
The maximum and the minimum values of z
To do this, we make use of graphical method.
Plot the constraints on a graph (see attachment)
Get the corner points from the points.
These are the points where [tex]x,y\ge 0[/tex]
So, we have:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (0,3)[/tex]
[tex](x_3,y_3) = (6,0)[/tex]
Substitute these points in the optimization equation:
[tex](x_1,y_1) = (0,0)[/tex]
[tex]z = 2x + 5y[/tex]
[tex]z = 2 * 0 + 5 * 0 = 0[/tex]
[tex](x_2,y_2) = (0,3)[/tex]
[tex]z = 2 * 0 + 5 * 3 = 15[/tex]
[tex](x_3,y_3) = (6,0)[/tex]
[tex]z = 2 * 6 + 5 * 0 = 12[/tex]
So, the values are:
Minimum = 0
Maximum = 15
Answer:
max= 16 min= -24
Step-by-step explanation:
Find the sample correlation coefficient for the following data.
X Y
3 8
7 12
5 13
9 10
11 17
13 23
19 39
21 38
a. .8911.
b. .9132.
c. .9822.
d. .9556.
Answer:
quneotentendeiporoqenouteetendxdin
Step-by-step explanation:
Help me to answer this.
Answer:
no solution
Step-by-step explanation:
If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?
Answer:
x=37.84
Step-by-step explanation:
We can write a ratio to solve
4 gallons 11 gallons
--------------- = ----------------
13.76 x dollars
Using cross products
4x = 11*13.76
4x=151.36
Divide by 4
4x/4 = 151.36/4
x=37.84
Can someone help me? I am struggling and I would be so happy if any of you helped me. Thank you for your help.
Answer:
mean=256229+253657+218747+246163+235626+288694+316265+196721+285077+215152+253291+315011+199901+265443+291806+303556+215359+258554+293658+289935÷21
=5198845÷21
=247564.0
=247564 to the next whole number
B.6 times
What is the true solution to the equation below? 2 lne^ln2x-lne^ln10x=ln30
It looks like the equation is
[tex]2\ln\left(e^{\ln(2x)}\right)-\ln\left(e^{\ln(10x)}\right) = \ln(30)[/tex]
Right away, we notice that any solution to this equation must be positive, so x > 0.
For any base b, we have [tex]b^{\log_b(a)}=a[/tex], so we can simplify this to
[tex]2\ln(2x)-\ln\left(10x\right) = \ln(30)[/tex]
Next, [tex]\ln(a^b)=b\ln(a)[/tex], so that
[tex]\ln(2x)^2-\ln\left(10x\right) = \ln(30)[/tex]
[tex]\ln\left(4x^2\right)-\ln\left(10x\right) = \ln(30)[/tex]
Next, [tex]\ln\left(\frac ab\right)=\ln(a)-\ln(b)[/tex], so that
[tex]\ln\left(\dfrac{4x^2}{10x}\right) = \ln(30)[/tex]
For x ≠ 0, we have [tex]\frac xx=1[/tex], so that
[tex]\ln\left(\dfrac{2x}5\right) = \ln(30)[/tex]
Take the antilogarithm of both sides:
[tex]e^{\ln\left((2x)/5\right)} = e^{\ln(30)}[/tex]
[tex]\dfrac{2x}5 = 30[/tex]
Solve for x :
[tex]2x = 150[/tex]
[tex]\boxed{x=75}[/tex]
someone please help
Answer:
28
Step-by-step explanation:
78
Consider the phrase "the sum of 3 times a number and the quotient of the number and 4." Let’s break it down. You want the sum of two values. The first value is 3 times a number. What expression represents 3 times a number?
9514 1404 393
Answer:
3x
Step-by-step explanation:
If x represents the number, then "3 times a number" is 3x.
__
Additional comment
"The quotient of the number and 4" is x/4.
The sum of those two expressions is ...
3x + x/4
If (-3)^-5 = 1/x, what is the value of x?
Answer:
-243
Step-by-step explanation:
(-3) (-3) (-3) (-3) (-3) = - 243
[tex]\frac{1}{-243 }[/tex]
As part of a statistics project, a teacher brings a bag of marbles containing 500 white marbles and 400 red marbles. She tells the students the bag contains 900 total marbles, and asks her students to determine how many red marbles are in the bag without counting them. A student randomly draws 100 marbles from the bag. Of the 100 marbles, 45 are red. The data collection method can best be described as
Answer:
Survey
Step-by-step explanation:
During data collection for a particular study, reaching all target Population might seem illogical or impossible. Therefore, a subset of the population of interest is chosen and the outcome used to infer about the population. This procedure could be referred to a a SURVEY. In the scenario samples drawn from the population of interest is used to make inference on population. During a survey, selected data ponuts or subjects must be drawn at random in other to ensure that it is representative of the larger population data.
Please help below with prob Stats
Answer:
te qif y btubf
Step-by-step explanation:
Two sides of a triangle have the same length. The third side measures 5 m less than twice the common length. The perimeter of the triangle is 23 m. What are the lengths of the three sides?
What is the length of the two sides that have the same length?
Answer:
Length of all 3 sides: 7, 7, and 9
Length of the two sides that have the same length: 7
Step-by-step explanation:
Let the two sides with equal lengths have a length of [tex]x[/tex]. We can write the third side as [tex]2x-5[/tex].
The perimeter of a polygon is equal to the sum of all its sides. Since the perimeter of the triangle is 23 meters, we have the following equation:
[tex]x+x+2x-5=23[/tex]
Combine like terms:
[tex]4x-5=23[/tex]
Add 5 to both sides:
[tex]4x=28[/tex]
Divide both sides by 4:
[tex]x=\frac{28}{4}=\boxed{7}[/tex]
Therefore, the three sides of the triangle are 7, 7, and 9 and the length of the two sides that have the same length is 7.
Write 4 with denominator 5
Answer:
4/5
Step-by-step explanation:
I'm not exactly sure what this question is asking but I'm guessing it's asking to create a fraction with the numerator as 4 and denominator as 5.
Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).
Answer:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope
1) Determine the slope
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-2, 6) and (3,-2):
[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
2) Plug in a point [tex](x_1,y_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
I hope this helps!
HELP PLEASE I DONT KNOW THIS ONE
Answer:
-3x^2 +7x -4
-------------------------------
(x-3)(x-2)(x+3)
Step-by-step explanation:
2 3x
-------- - ----------
X^2-9 x^2 -5x+6
Factor
2 3x
-------- - ----------
(x-3)(x+3) (x-3)(x-2)
Get a common denominator
2 (x-2) 3x(x+3)
-------- - ----------
(x-3)(x+3)(x-2) (x-3)(x-2)(x+3)
2x-4 - (3x^2 -9x)
-------------------------------
(x-3)(x-2)(x+3)
Distribute
2x-4 - 3x^2 +9x
-------------------------------
(x-3)(x-2)(x+3)
Combine like terms
-3x^2 +7x -4
-------------------------------
(x-3)(x-2)(x+3)
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{gold}{Answer \red{:)}}}}}}}}[/tex]
[tex]\sf{\dfrac{2}{ x^2-9}-\dfrac{3x}{x^2-5x+6}}[/tex] [tex]\sf{\dfrac{2}{ (x)^2-(3)^2}-\dfrac{3x}{x^2-2x-3x+6} }[/tex] [tex]\sf{\dfrac{2}{(x+3)(x-3)}-\dfrac{3x}{x(x+2)-3(x+2)} }[/tex][tex]\sf{\dfrac{2}{(x+3)(x-3)}-\dfrac{3x}{(x+2)(x-3)}}[/tex][tex]\sf{\dfrac{2(x-2)-3x(x+3)}{(x+3)(x-2)(x-3)} }[/tex] [tex]\sf{\dfrac{2x-4-(3x^2-9x)}{(x+3)(x-2)(x-3) }}[/tex] [tex]\sf{\dfrac{2x-4-3x^2+9x}{(x+3)(x-2)(x-3) }}[/tex] [tex]\sf{\dfrac{-3x^2+7x-4}{(x+3)(x-2)(x-3) }}[/tex][tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
9 3/5 % as a decimal, rounded to 3 decimal places, is:
Answer:
0.054
Step-by-step explanation:
9 3/5% as a decimal is 0.054 (already to 3 decimal places)
Answer from Gauthmath
9 are just, well..., 9
3/5 are 0.6
because 1/5 is 0.2
so it's 9.6%, not so complicated I guess
Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2
Answer:
A. -510
Step-by-step explanation:
We are given the variable values:
a = -2r = 2n = 8Geometric series formula:
[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]
Plugging in values we have:
[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]
Simplifying the equation we are left with:
[tex] \frac{ - 2(255)}{1} = - 510[/tex]
The function f(x)=log4x is dilated to become g(x)=f(13x).
What is the effect on f(x)?
Answer:
f(x) is compressed horizontally
Step-by-step explanation:
Given
[tex]f(x) = \log(4x)[/tex]
[tex]g(x) = f(13x)[/tex]
Required
The effect on f(x)
[tex]g(x) = f(13x)[/tex] implies that f(x) is horizontally compressed by 13.
So, we have:
[tex]f(13) = \log(4 * 13x)[/tex]
[tex]f(13) = \log(52x)[/tex]
So:
[tex]g(13) = \log(52x)[/tex]
Find the formula for the geometric sequence 4, 20, 100, 500, ...
Answer:
2500
Step-by-step explanation:
it is a geometric progression
r=5
The geometric sequence 4, 20, 100, 500 is [tex]\rm a_n = 4 \times 5^{n-1}[/tex].
What is the geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.
This ratio is known as a common ratio of the geometric sequence.
The given geometric sequence 4, 20, 100, 500.
The common difference between the geometric sequence is;
[tex]\rm \dfrac{a_2}{a_1}=\dfrac{20}{4} =5\\\\ \dfrac{a_3}{a_2}=\dfrac{100}{20} =5\\\\ \dfrac{a_4}{a_3}=\dfrac{500}{100} =5\\\\[/tex]
The formula geometric sequence is;
[tex]\rm a_n = a_1 \times r^{n-1}\\\\ a_n = 4 \times 5^{n-1}[/tex]
Where a1 is the first term and r is the common difference of the given geometric sequence.
Hence, the geometric sequence 4, 20, 100, and 500 is [tex]\rm a_n = 4 \times 5^{n-1}[/tex].
Learn more about geometric sequence here;
https://brainly.com/question/15486558
#SPJ2
You wish to create a 5 digit number from all digits; 0 1 2 3 4 5 6 7 8 9
Repetition is not allowed
* 0 cannot be first as it does not count as a place value if it is first. Ie. 027 is a 2 digit number
How many even numbers can you have?
Answer:
10234
Step-by-step explanation:
one is the smallest number so its first
and then you can place zero
after that just place the second smallest number
and so on
Enter the numb bee that belongs in the green box
this is the answer
210.28
One year the ACT had a mean score of 21.2 and a standard deviation of 5.1. That same year, the SAT had a mean score of 1498 and a standard deviation of 347. Suppose that a scholarship committee is considering two students, one who scored 26 on the ACT and another who scored 1,800 on the SAT. Both are pretty good scores, but which one is better? Find the z-score for the ACT
Answer:
ACT Score performed better.
Step-by-step explanation:
Given :
ACT :
Mean score, μ = 21.2
Standard deviation, σ = 5.1
Score, x = 26
SAT :
Mean score, μ = 1498
Standard deviation, σ = 347
Score, x = 1800
To know which score is better, we obtain the standardized, Z score of the two examination :
Zscore = (x - μ) / σ
ACT Zscore :
(26 - 21.2) / 5.1
Zscore = 4.8 / 5.1 = 0.941
ACT Zscore = 0.941
SAT Zscore :
(1800 - 1498) / 347
Zscore = 302 / 347 = 0.870
SAT Zscore = 0.870
The student with the higher Zscore performed better :
ACT Zscore > SAT Zscore
125. Albert surveyed a class of 25 students on sports. 5 kids love baseball. 7 kids love basketball. 10 kids
love football. How many students did not like baseball, basketball, or football?
25 students
12 students
22 students
3 students
Answer:
3 students
Step-by-step explanation:
since the total number of students is 25,when you add those that like baseball, basketball and football the total number must be 25 but in this case it's 22 meaning 2 student liked neither.
7+5+10+x=25
x=25-22
=3
I hope this helps
6. Solve for x: 3|x - 7| = 15
Please give steps! ❤️
3 | x - 7 | = 15
Divide both sides by 3
3 | x - 7 | ÷ 3 = 15 ÷ 3
| x - 7 | = 5
_________________________
" Reminder "
| a | = t ===》 a = + t OR a = - t
__________________________
| x - 7 | = 5
x - 7 = 5 ====》 x = 12
OR
x - 7 = - 5 ===》 x = 2
A bag contains 9 red balls numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 6 white balls numbered 10, 11, 12, 13, 14, 15. One ball is drawn from the bag. What is the probability that the ball is white, given that the ball is even-numbered
Answer:
3/ 7
Step-by-step explanation:
We know that it is an even ball
2,4,6,8,10,12,14 are even balls
2,4,6,8 are red and 10,12,14 are white
P ( white) = white even / total even
= 3/ 7
Simplify
x * x^5 / x^2 * x
fastest answer gets brainiest !
Which data value has the highest frequency?
116
316
38
58
Answer:
A. 1/16Step-by-step explanation:
The most repeated value is:
(1/4)/4 = 1/16There are 4 of them.
Correct choice is A