Answer:
[tex]\sf x=\frac{1}{10}[/tex]
Step-by-step explanation:
Rewrite expression with bases of 4.
[tex]\sf{4^{\frac{3}{4} }} \times \sf({4^\frac{1}{2} )^x =(4^2)^{\frac{2}{5} }[/tex]
Apply law of exponents, when bases are same for exponents in multiplication, add the exponents. When a base with an exponent has a whole exponent, then multiply the two exponents.
[tex]\sf{4^{\frac{3}{4} }} \times \sf{4^{\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]
[tex]\sf{4^{\frac{3}{4} +\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]
Cancel same bases.
[tex]\sf \frac{3}{4} +\frac{1}{2} x=\frac{4}{5}[/tex]
Subtract 3/4 from both sides.
[tex]\sf \frac{1}{2} x=\frac{1}{20}[/tex]
Multiply both sides by 2.
[tex]\sf x=\frac{1}{10}[/tex]
Step-by-step explanation:
2^{2*3/4} × 2^{x}=2^{4×2/5}
2^{3/2} × 2^{x}= 2^{8/5}
2^{3/2+x}=2^{8/5}
equate powers
{3+2x}/2= 2^2
5{3+2x}= 2{8}
15+10x=16
collect like terms
10x=16-15
10x=1
divide both sides by 10
x=1/10
x=0.1
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet.
When the water was 4 feet from the end of the hose, what was its height above the ground?
3.2 feet
4.8 feet
5.6 feet
6.8 feet
Answer: A) 3.2 ft
Step-by-step explanation:
f(4) = -0.3(4)² + 2(4)
= -4.8 + 8
= 3.2
Answer:
3.2 feet
Step-by-step explanation:
Assume that adults have it scores that are normally distributed with a mean of 99.6 and a standard deviation of 16.2 find the first quartile which is the hw score sepedafinf the bottom 25%
Answer:
88.7
Step-by-step explanation:
P(Z < z) = 0.25
z = -0.674
z = (x − μ) / σ
-0.674 = (x − 99.6) / 16.2
x = 88.7
50 Pts!! Brainliest!! Answer ASAP, thx.
Answer:
1/625
Step-by-step explanation:
When you multiply, you add the exponents. You now have [tex]6^{-4}[/tex]. This is equivalent to [tex]\frac{1}{5^{4} }[/tex] which equals 1/625.
Answer:
1/625
Step-by-step explanation:
5^ -1 * 5^-3
The bases are the same, so we can add the exponents
5^ (-1+-3)
5^-4
We know that a^-b = 1/ a^b
1/5^4
1/625
True or False: The proportion of the population that has certain characteristics is the same as the probability that a randomly selected individual of the population has these same characteristics.
Answer:
True
Step-by-step explanation:
What is the result of 36 divided by 9? Use the number line to find the answer.
Answer:
4
Step-by-step explanation:
In the diagram, PQRT is a rhombus. STUQ and
PUR are straight lines. Find the values of x and y.
Step-by-step explanation:
since PQRT is a rhombus,
URQ=TPU
y=180-90-24=66
x=180-32-90-24=34
Suppose I have either a fair coin or a bent coin, and I don’t know which. The bent coin has a 60 % 60\% 60% probability of coming up heads. I throw the coin ten times and it comes up heads 8 times. What is the probability I have the fair coin vs. the probability I have the bent coin? Assume at the outset there is an equal ( . 5 , . 5 ) (.5,.5) (.5,.5) prior probability of either coin.
Answer:
the Probability of Fair coin = 0.2664=26.64 % and
Probability of Bent coin = 0.7336= 73.36 %
Step by step Explanation:
The fair coin has a 60% probability of coming up heads, same thing with the bent coin , when the coin was thrown up ten times,it comes up heads 8 times,
Here we were told to find the probability fair coin vs. probability bent coin
A)THE FAIR COIN::
The probability of getting Head Coin = 1/2
Probability of getting tail Coin = 1/2
Then the Probability of head 8 times out of 10 can be calculated using combination
= ¹⁰C₈ × (1/2)⁸ ×(1/2)²
= 45/1024
= 0.0439
Therefore, the Probability of head 8 times out of 10= 0.0439
B)BENT COIN
the probability of getting Head Coin = 0.6
= 6/10
= 3/5
NOTE: 60%=0.6
The probability of getting tail Coin = 1 - 3/5
= 2/5
Then, the probability of getting head 8 times out of 10 can be calculated using combination;
= ¹⁰C₈ × (3/5)⁸ × (2/5)²
= 45 × 6561 ×( 4 / 5¹⁰)
= 0.1209
Therefore, the probability of getting head 8 times out of 10 = 0.1209
We can now calculate the Probability of Fair coin
(Probability of head 8 times out of 10 in fair coin )/(Probability of head 8 times out of 10 in fair coin )+(the probability of getting head 8 times out of 10 in bent coin)
= (0.0439 )/(0.0439 + 0.1209)
= 0.2664
Probability of bent coin can as well be calculated as 0.1209 /(0.0439 + 0.1209)
= 0.7336
Therefore, the Probability of Fair coin = 0.2664=26.64 % and
Probability of Bent coin = 0.7336= 73.36 %
What is the surface area of the right cone below?
A. 52 units2
O B. 1047 units2
C. 6870 units2
D. 5471 units2
First find height using Pythagorean theorem.
[tex]h^2+4^2=13^2\implies h=\sqrt{153}\approx12.37[/tex].
Then use cone surface area formula and compute the result:
[tex]A=\pi r(r+\sqrt{h^2+r^2})\approx\boxed{68\pi}\mathrm{units^2}[/tex].
Hope this helps.
Aster corporation accepted a $20,000, 9 percent 120-day note dated august 25 from lee company in settlement of a past bill. On October 25, Aster Corporation decided to discount the note at a discount of 8 percent. The proceeds to Aster Corporation are (blank)
Answer:
$20, 533.33
Step-by-step explanation:
From the question, we are given the following values
Principal = $20000
Rate = 8% = 0.08
Time( in years) = 120days = 4 months = 4/12 years = 1/3 years
Interest = Principal × Rate × Time
Interest = 20,000 × 0.08× (1/4)
Interest = $533.33
Hence, the proceeds to Aster Corporation are
$20000 + $533.33
= $20,533.33
Your brother has a bag of marbles. He has 8 green marbles, 3 blue marbles, 7 red marbles, and 2 yellow marbles. What is the ratio of blue marbles to green and red marbles? Choose the answer that is a simplified unit rate. a 1 : 5 b 3 : 15 c 5 : 1 d 15 : 3
Answer:
a 1 : 5
Step-by-step explanation:
Blue mables: 3
green and red marbles: 8 + 7 = 15
then, the radio blue:(green+red) is:
3 : 15
simplified unit rate is:
3/3 = 1
15/3 = 5
then:
3:15
is equal to:
1:5
Answer:
a 1 : 5
In 2002, the mean expenditure for auto insurance in a certain state was $806. An insurance salesperson in this state believes that the mean expenditure for auto insurance is less today. She obtains a simple random sample of 32 auto insurance policies and determines the mean expenditure to be $781 with a standard deviation of $39.13. Is there enough evidence to support the claim that the mean expenditure for auto insurance is less than the 2002 amount at the α = 0.05 level of significance?
Answer:
No there is not enough evidence to support the claim that the mean expenditure for auto insurance is less than the 2002 amount at the α = 0.05 level of significance
Step-by-step explanation:
Sample Mean = μ1 = $806
Sample Mean = μ2 = $ 781
Standard Deviation= S= σ =39.13
n= 32
Confidence Interval = 95 %
α= 0.05
z∝=± 1.96
We state the null and alternative hypotheses as
H0: μ1 = $806 and Ha: μ1 ≠ $806 two sided tail test
z= μ1 -μ2/σ/√n
z= 806-781/ 39.13/√32
z= 806-781/ 39.13/5.6568
z=806-781/ 6.92
z= 25/6.92
z= 3.613
Z> z∝
3.613 > ± 1.96
No there is not enough evidence to support the claim that the mean expenditure for auto insurance is less than the 2002 amount at the α = 0.05 level of significance
The tee for the sixth hole on a golf course is 305 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
Correct answer is option D. 96.4 yd.
Step-by-step explanation:
Please refer to the attached figure for labeling of the given diagram.
ABC is a triangle with the following labeling:
A is the hole, B is the Tee and C is the point where the ball is.
Sides are labeled as:
[tex]a =255\ yd\\c = 305\ yd\\\angle B =17^\circ[/tex]
To find:
Side [tex]b = ?[/tex]
Solution:
Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.
We can use cosine formula here to find the value of the unknown side.
[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]
Putting all the values:
[tex]cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd[/tex]
So, the distance between the Ball and hole is 96.42 yd
Correct answer is option D. 96.4 yd.
Answer:
D.) 96.4 yd
Step-by-step explanation:
I got it correct on founders edtell
A double-blind experiment was conducted to evaluate the success of a Zika virus vaccine. What is the purpose of keeping treating physicians unaware of
the treatment status of the experimental subjects?
To eliminate grounds for malpractice suits
To ensure subjects were assigned randomly to treatments
To remove a possible source of bias
To make sure nobody is injured
To avoid the placebo effect
To remove a possible source of bias
Step-by-step explanation:
If the test subjects know they are part of an experiement, this could cause them to think that it worked and it could either lead to untruthful answers or the test subjects tricking themselves to think that the vaccine worked
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
C: [tex]\lim_{x \to 0} y \to -\infty[/tex]
Step-by-step explanation:
The y-axis is the asymptote, and G(x) approaches it as x is getting smaller and smaller.
Actually, even more accurate would be to write
[tex]\lim_{x \downarrow 0} y \to -\infty[/tex]
The down arrow shows that x has to approach 0 from the positive side.
if sade can be 12 years and his mother senior him with 24 years and his dad senior him with 30 yearshow old is the sum of the both parents
Answer:
88
Step-by-step explanation:
mother's age = 12+24
= 36
father's age = 12+40
=52
add the parent age= 36+52
= 88
If a sprinkler waters 1/15 of lawn in 1/5 of an hour how much time will it take to water the entire lawn ?
Answer:
3 hours
Step-by-step explanation:
1/5 of an hour would be equivalent to 12 minutes (60 minutes in an hour divided by 5)
Multiply 12 minutes by 15 to see how long it will take to water the entire lawn in minutes ----> 12x15=180
Divide 180 by 60 to see how many hours it takes ---> 180/60=3
Answer:
3 hours.
Step-by-step explanation:
1/15 of the lawn is watered in 1/5 hours
So the whole lawn is watered in 15 * 1/5
= 3 hours.
PLEASE HELP BRAINLY INSTANTLY
Kira solved the equation in the following way.
7/2 − 2x = 11/2
7/2 − 7/2 − 2x = 11/2 − 7/2
−2x ÷ −2 = 4/2 ÷ − 2
x = −1 Describe the properties of equality that Kira used. The first step is to use the ____ property of equality to combine the constant terms. The second step is to use the ___ property of equality to isolate the variable.
Answer:
subtraction; division
Step-by-step explanation:
the first step is to subtract 7/2 from both sides.
the second step is to divide by -2
Answer:
✔ Subtraction
✔ Division
Step-by-step explanation:
It's right in Edgen
how do i solve for this help please \sqrt(x+5) = \sqrt(x)+1
Answer:
x=4
Step-by-step explanation:
sqrt(x+5) = sqrt(x)+1
Square each side
(sqrt(x+5))^2 = (sqrt(x)+1)^2
x+5 = (sqrt(x)+1)^2
Foil
x+5 = (sqrt(x)) ^2 + sqrt(x) + sqrt(x) + 1
x+5 = x + 2 sqrt(x) + 1
Subtract x from each side
5 = 2 sqrt(x) + 1
Subtract 1 from each sdie
4 = 2 sqrt(x)
Square each side
4^2 = (2 sqrt(x))^2
16 = 4 x
Divide by 4
16/4 = 4x/4
4 =x
Check to see if it is extraneous
sqrt(4+5) = sqrt(4)+1
sqrt(9) = sqrt(4) +1
3 = 2+1
3=3
It is a valid solution
Answer:
[tex]\boxed{x=4}[/tex]
Step-by-step explanation:
[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]
Take the square on both sides.
[tex]x+5=( \sqrt{x}+1)^2[/tex]
Expand brackets.
[tex]x+5=( \sqrt{x}+1) ( \sqrt{x}+1)[/tex]
[tex]x+5= \sqrt{x} ( \sqrt{x}+1) +1 ( \sqrt{x}+1)[/tex]
[tex]x+5= x+ \sqrt{x}+ \sqrt{x}+1[/tex]
[tex]x+5= x+ 2 \sqrt{x}+1[/tex]
Subtract 2√x, x, and 5 on both sides.
[tex]x- 2 \sqrt{x} -x= 1-5[/tex]
[tex]-2 \sqrt{x} = -4[/tex]
Cancel negative signs.
[tex]2\sqrt{x} = 4[/tex]
Divide both sides by 2.
[tex]\sqrt{x} =2[/tex]
Square both sides.
[tex]x=2^2[/tex]
[tex]x=4[/tex]
Check if the solution in the equation works.
[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]
Let [tex]x=4[/tex]
[tex]\sqrt{4+5} = \sqrt{4}+1[/tex]
[tex]\sqrt{9} = 2+1[/tex]
[tex]3=3[/tex]
The value of x as 4 works in the equation.
Five boxes of crackers cost 9$. At this rate, how much do 20 boxes cost?
Answer:36
Step-by-step explanation: first I did
9÷5=1.80 per box.
so then I did 1.80 x 20 which = 36
Answer:
20 boxes cost $36
Step-by-step explanation:
Using proportions,
5 boxes cost 9$
20 boxes cost X$
Cross multiply
X = 9/5 * 20 = 36$
Any help on this???????????
Answer:
x = 121°
Step-by-step explanation:
The angle supplementary to 115° is 180 - 115 = 65° and the angle that forms a full circle with 304° is 360 - 304 = 56°. Since the measure of an exterior angle is equal to the sum of its remote interior angles, we know that x = 65 + 56 = 121°.
select the coordinates of two points on the line y = -2
Answer: (0, -2) & (1, -2)
Step-by-step explanation:
There are an infinite number of coordinates on y = -2.
The coordinates can have any x-value, but must have -2 for the y-value.
2. Find the distance between the two points. Round to the nearest tenth if necessary.
(0,9), (-8, -4)
21
15.3
9.4
233
Answer:
[tex]\boxed{D = 15.8\ units}[/tex]
Step-by-step explanation:
The coordinates are (0,9) and (-8,-4)
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
D = [tex]\sqrt{(-8-0)^2+(-4-9)^2}[/tex]
D = [tex]\sqrt{(-8)^2+(-13)^2}[/tex]
D = [tex]\sqrt{81+169}[/tex]
D = [tex]\sqrt{250}[/tex]
D = 15.8 units
Answer:
15.3
Step-by-step explanation:
The coordinates are (0,9) and (-8,-4)
Distance of two points formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Plug in the values.
[tex]D=\sqrt{(-8-0)^2+(-4-9)^2}[/tex]
[tex]D=\sqrt{(-8)^2+(-13)^2}[/tex]
[tex]D=\sqrt{64+169}[/tex]
[tex]D=\sqrt{250}[/tex]
[tex]D= 15.264338...[/tex]
[tex]D \approx 15.3[/tex]
3 - 2x is a polynomial
Answer:
true
Step-by-step explanation:
3 -2x is a polynomial of degree 1, consisting of two terms. Such a polynomial can be referred to as a "binomial."
Your observation is True.
What is 651 minus -13? Please with explanation.
Answer:
664
Step-by-step explanation:
651 - - 13
Negative times negative is positive.
651 + 13
Add.
664
Answer:
664
Step-by-step explanation:
651 - (-13)
Do the keep , change , change method
So , it will be :
651 + 13 = 664
Hope this helps and plsss plss amrl as brianliest and THNXX :)
Which statements are true regarding undefinable terms in geometry?
C. A line has one dimension, length.
E. A plane consists of an infinite set of lines.
2.) Evaluate 6a² if a = 4
Answer:
96
Step-by-step explanation:
We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.
A line has____ rotational symmetry. A. Four-fold B. Six-fold C. Two-fold D. Seven-fold
Answer:
Option C
Step-by-step explanation:
A line has a 2-Fold rotational symmetry because if we rotate the line about 180, The resulting thing will be the same line.
Answer:
[tex]\boxed{\mathrm{C}}[/tex]
Step-by-step explanation:
A line has two-fold rotational symmetry.
The line rotated two times from a central point remains the same.
Or the line rotated 180 degrees from a central point remains the same.
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answer:
3x (x - 2) (x + 3)
Answer 4
Hope this helps :)
which equation can be used to find the length of AB
Answer:
B
Step-by-step explanation:
You have to use cos because you are using the adjacent and hypotenuse
So
cos38=x/14
multiply each side by 14
14cos38
Solve for the unknown angles. Justify your answers.
Answer:
1. 31.67 degrees
2. 38 degrees
3.
PNQ = 117 degrees
LKQ = 102 degrees
4. XYV = 120 degrees
Step-by-step explanation:
1. Using sum of angles of a triangle = 180
angle ACB = 180 - 55.14 - 93.19 = 31.67
2.
FDE = 180-GDE = 180 - 135.11 = 44.89 [angles on a line are supplementary]
FED = HEJ = 97.11 [vertical angles]
DFE = 180-FDE-FED = 180 - 44.89 - 97.11 = 38 degrees
3.
MLN = 180 - 82 = 98 [angles on a line are supplementary]
PNQ = 360 - 67 - 78 - 98 = 117 [sum of exterior angles of a polygon = 360]
LKQ = 180 - 78 = 102 [angles on a line are supplementary]
4.
WXY+YXZ = 180 [angles on a line are supplementary]
=>
3x + x = 180
=>
x = 180/4 = 45
Now solve for XYV
XYV = 360 - 135 - 60 - 45 = 120 [sum of interior angles of quadrilateral = 360]
Note: In the future, please limit the number of problems per question to three.