[tex]\displaystyle\bf 2^{2x+1}-9\cdot 2^x+4=0 \quad ; \qquad \boxed{ 2^x=t \; ; \; 2^{2x}=t^2} \\\\2t^2-9t+4=0 \\\\D=81-32 =49 \\\\ t_1=\frac{9+7}{4} =4 \\\\ t_2=\frac{9-7}{4} =\frac{1}{2} \\\\1) \ 2^x=4 \Longrightarrow x_1=2 \qquad 2) \ 2^x=2^{-1}\Longrightarrow x_2=-1 \\\\Answer: \boxed{x_1=2 \quad ; \quad x_2=-1}[/tex]
Find the equation of the line through point (2,2) and parallel to y=x+4. Use a forward slash (i.e.”/“) for fractions (e.g. 1/2 for
Answer:
The equation of the line is, y = x
Step-by-step explanation:
The constraints of the required linear equation are;
The point through which the line passes = (2, 2)
The line to which the required line is parallel = y = x + 4
Two lines are parallel if they have the same slope, therefore, we have;
The slope of the line, y = x + 4 is m = 1
Therefore, the slope of the required line = 1
The equation of the required lime in point and slope form becomes;
y - 2 = 1 × (x - 2)
∴ y = x - 2 + 2 = x
The equation of the required line is therefore, y = x
College national study finds that students buy coffee from a coffee shop on average 12 times a week, I believe it may be different for UML students. I collect data from a sample of 36 UML students and find that they buy coffee on average 8 times a week, with a standard deviation of 6 days. What is the T value for this data, and can you reject the null?
Answer:
The t-value for this data is -4.
The p-value of the test is 0.0003 < 0.05, which means that the null hypothesis can be rejected.
Step-by-step explanation:
College national study finds that students buy coffee from a coffee shop on average 12 times a week, I believe it may be different for UML students.
At the null hypothesis, we test if the mean is of 12, that is:
[tex]H_0: \mu = 12[/tex]
At the alternative hypothesis, we test if the mean is different of 12, that is:
[tex]H_1: \mu \neq 12[/tex]
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
12 is tested at the null hypothesis:
This means that [tex]\mu = 12[/tex]
I collect data from a sample of 36 UML students and find that they buy coffee on average 8 times a week, with a standard deviation of 6 days.
This means that [tex]n = 36, X = 8, s = 6[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{8 - 12}{\frac{6}{\sqrt{36}}}[/tex]
[tex]t = -4[/tex]
The t-value for this data is -4.
P-value of the test:
Considering a standard significance level of 0.05.
Test if the mean is different from a value, so two-tailed test, with 36 - 1 = 35 df and t = -4. Using a t-distribution calculator, the p-value is of 0.0003.
The p-value of the test is 0.0003 < 0.05, which means that the null hypothesis can be rejected.
If < A and < B form a linear pair, and < A = x - 13 degrees, and < B = x + 7 degrees, then find x.
Select one:
a. 124
b. 101
c. 46
d. 93
Answer:
d
Step-by-step explanation:
A linear pair sum to 180° , then
x - 13 + x + 7 = 180
2x - 6 = 180 ( add 6 to both sides )
2x = 186 ( divide both sides by 2 )
x = 93 → d
What percent of 45 is 27
Answer:
60%
Step-by-step explanation:
27/45 = .6
.6 = 60%
Identify the equation of the line that is perpendicular to =12−7 and runs through point (4,−2). Group of answer choices
Answer:
12y+x = -20
Step-by-step explanation:
Question restructured
Identify the equation of the line that is perpendicular to y =12x−7 and runs through the point (4,−2).
The equation of a line in point-slope form is expressed as;
y-y0 = m(x-x0)
m is the slope
(x0,y0) is a point on the line
Given the equation y = 12x - 7
Slope = 12
Since the required line is perpendicular to this line, the slope of the required line will be;
m = -1/12
Get the required equation
y-(-2) = -1/12 (x - 4)
y+2= -1/12(x-4)
Cross multiply
12(y+2) = -(x-4)
12y+24 = -x+4
12y + x = 4-24
12y+x = -20
Hence the required equation is 12y+x = -20
NB: The equation of the line used in question was assumed
5 positive integers are arranged in ascending order, as follows:
1,9, 9, 10, X
The mean and the median are equal.
Find X.
Answer:
x = 16
Step-by-step explanation:
Since the numbers are in ascending order, x is the number with the highest value here.
From the arrangement, we can see that the median (the middle number) is the third number which is 9
The mean is the sum of the numbers divided by their count. So we set up the mean and equate to the median
We have this as;
(1 + 9 + 9 + 10 + x)/5 = 9
29 + x = 5(9)
29 + x = 45
x = 45-29
x = 16
39/50 as a percentage?
Answer:
78%
Step-by-step explanation:
39/50×100%
= 39×2%
= 78%
Answered by GAUTHMATH
Answer:
78%
Step-by-step explanation:
Divide 39 by 50 and then multiply by 100 and you get the percentage and that goes for all fractions if you wanna change them into percent form. If you want it to be decimal just don't multiply the 100 at the end.
What is the next term in the sequence below?
24, 12, 6, 3, . . .
A. 0.5
B. 1.5
C. 1.75
D. 2.5
Answer:
1.5(B)
Step-by-step explanation:
This is a geometric sequence where each number is 1/2 times the last. So 3/2 is 1.5.
can someone help me with this please
Answer:
for question B
2A 3C = 70
70-15 = 55/5 = 11.
so each child is 11
while adult 11 + 7.50 = 18.50
if the sum is 4 and one of the integers is 1 what must the other integer be
Step-by-step explanation:
The answer to the question is 3
Answer:
3
Step-by-step explanation:
1 + X = 4
4 - 1 = X
3 = X
brianliest!! 10 point!! hurry pls!!
Answer:
your answer is totally correct
help help help pls :)
Answer:
[tex]opposite\approx 70.02[/tex]
Step-by-step explanation:
The triangle in the given problem is a right triangle, as the tower forms a right angle with the ground. This means that one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are as follows;
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Please note that the names ([tex]opposite[/tex]) and ([tex]adjacent[/tex]) are subjective and change depending on the angle one uses in the ratio. However the name ([tex]hypotenuse[/tex]) refers to the side opposite the right angle, and thus it doesn't change depending on the reference angle.
In this problem, one is given an angle with the measure of (35) degrees, and the length of the side adjacent to this angle. One is asked to find the length of the side opposite the (35) degree angle. To achieve this, one can use the tangent ([tex]tan[/tex]) ratio.
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Substitute,
[tex]tan(35)=\frac{opposite}{100}[/tex]
Inverse operations,
[tex]tan(35)=\frac{opposite}{100}[/tex]
[tex]100(tan(35))=opposite[/tex]
Simplify,
[tex]100(tan(35))=opposite[/tex]
[tex]70.02\approx opposite[/tex]
A roller coaster starts at point A. It goes up 20 feet, down 32 feet, and then up 16 feet to point B. Write an addition sentence to find the height at point B in relation in point A.
Heklp po pasahan na bukas
Answer:
20+(-32)+16
Step-by-step explanation:
It goes up which is positive then goes down which is negative then goes back up which is positive
What is the value of y in the equation y = 3x - 2. whenx = 2? *
Answer:
4
Step-by-step explanation:
y=3x-2
y=3(2)-2
y=6-2
y=4
Choose the correct answer from the given four options:The 21st term of the AP whose first two terms are –3 and 4 is
17
-137
137
127
Answer:
137
Step-by-step explanation:
given AP
t1 = -3 and t2 = 4
using,
d=t1-t2
=4-(-3)
=7
And,
tn=a+(n-1)d
t21=(-3)+(21-1)(7)
t21=137
Answer:
B) -137
Step-by-step explanation:
a=a1=−3,a2=4
∴d=a2−a1=4−(−3)=4+3=7
What is the solution to the equation below. Round your answer to two
decimal places
In x= 3.1
The solution to the equation below rounded to 2 decimal places is 22.20.
How to simplify logarithmic equations?Given the logarithmic expressions
ln x = 3.1
We are to determine the value of "x"
ln x = 3.1
Take the exponent of both sides
e^ln x = e^3.1
The exponent will cancel out the log function to have:
x = e^3.1
x = 22.197
Hence the solution to the equation below rounded to 2 decimal places is 22.20.
Learn more on log function here: https://brainly.com/question/1695836
Use the equation of the water level of the river represented by the equation y = −4x + 170, where x represents the number of years and y represents the total feet. What points are located on the line? Check all that apply. (170, 0) (0, 170) (12, 126) (50, 30) (5, 150) (60, –70)
Answer:
(0, 170) (5, 150) (60, -170)
Step-by-step explanation:
Plug each x value into the equation. The point is located on the line if the y values match.
Ex. -4 (170) + 170 = -510 this point is not on the line
-4 (0) + 170 = 170 this point is on the line because it is a "true" statement
Answer:
(0, 170) (5, 150) (60, -170)
Step-by-step explanation:
What's a boxplot? Also provide an example...
Answer:
BOXPLOT is a simple way of representing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, usually with a vertical line inside to indicate the median value. The lower and upper quartiles are shown as horizontal lines either side of the rectangle.
Step-by-step explanation:
Example 1: Draw a box-and-whisker plot for the data set {3, 7, 8, 5, 12, 14, 21, 13, 18}.
From our Example 1 on the previous page, we had the five-number summary:
Minimum: 3, Q1 : 6, Median: 12, Q3 : 16, and Maximum: 21.
CHECK THE ABOVE PICNotice that in any box-and-whisker plot, the left-side whisker represents where we find approximately the lowest 25% of the data and the right-side whisker represents where we find approximately the highest 25% of the data. The box part represents the interquartile range and represents approximately the middle 50% of all the data. The data is divided into four regions, which each represent approximately 25% of the data. This gives us a nice visual representation of how the data is spread out across the range.
Step-by-step explanation:
In descriptive statistics, a box plot or boxplot (also known as box and whisker plot) is a type of chart often used in explanatory data analysis. Box plots visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 25.540 degrees
Step-by-step explanation:
When computing the value of x, there are various ways to solve with given information.
The easiest way is to set up the equation: cos(20 degrees) = 24/x
Cosine is adjacent over the hypotenuse.
Multiplying x on both sides, and dividing by cos(20 degrees), we are left with x = 24/cos(20 degrees).Solving for it in a calculator, we are left with 25.540 degrees.What is the area, in square inches, of the trapezoid below
Answer:
89.2 in^2
Step-by-step explanation:
1/2(15.7+6.6)(8)
=89.2 in^2
Answer:
A = 89.2 in²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 8, b₁ = 6.6, b₂ = 15.7 , then
A = [tex]\frac{1}{2}[/tex] × 8 × (6.6 + 15.7) = 4 × 22.3 = 89.2 in²
In a clinic, a doctor charges Rs 1200 for every 15 minutes. If he attends to the clinic 2 hours per day for seven days, how much will he earn during a week?
Answer:
67,200 (please note you did not specify the currency this is figured in so that is important to include in your answer. If this answer is in dollars, then make sure you add a dollars sign and specify "dollars" in your answer. If it is in another currency then put that in).
Step-by-step explanation:
First, we need to figure out how much the doctor makes per hour. Since there are 4, 15 minute billing periods per hour, we multiple to find the hourly billing charges:
4[tex]4*1200=4800[/tex] (this is the amount the doctor makes per hour)
Next, we have to take that hourly charge and multiply it by 2 because we know the doctor works two hours per day:
[tex]4800*2=9600[/tex] (this is the amount the doctor makes per day working two hours)
Finally, we know the doctor attends to the clinic two hours per day and seven days per week. We have to multiply the amount of money earned in two hours (9600) by 7 days:
[tex]9600*7=67,200[/tex] (this is the amount the doctor makes in seven days, billing two hours per day)
Do you agree? Explain why or why not.
Answer:
if x = 4
[tex]\sqrt{8 + 1} + 3 = 0[/tex]
[tex]\sqrt{9} + 3 = 0[/tex]
3 + 3 = 0
6 = 0
wrong.
Use the elimination method to solve the system of equations
2x+3y=8
x-y=9
Answer:
Step-by-step explanation:
Answer: x = 7 and y = -2
Step-by-step explanation:
2x +3y = 8 ----------------(1)
x-y = 9 ----------------------(2)
multiply (2) by 2
2x-2y = 18--------------------(3)
subtract (2) from (3)
-5y = 10
Divide bothside by -5
y = -2
Similarly, multiply (2) by 3
3x-3y = 27-----------------------(4)
add (1) and (4) together
5x = 35
Divide bothside by 5
x= 7
Therefore, x =7 and y= -2
A girl walked 6km from her house to a market and discovered that she had covered 4/5 of the distance to the market how far is the market from her house
Answer: [tex]7.5\ km[/tex]
Step-by-step explanation:
Given
Girl has traveled 6 km from her house
She has covered [tex]\frac{4}{5}[/tex] of the distance
Suppose the total distance is x
[tex]\therefore 6=\dfrac{4x}{5}\\\\\Rightarrow x=\dfrac{30}{4}\\\\\Rightarrow x=\dfrac{15}{2}\ \text{km}\\\\\Rightarrow x=7.5\ \text{km}[/tex]
Find the value of x.
16.2
0.03
38.5
34.8
Hi there!
[tex]\large\boxed{x = 38.5}}[/tex]
To solve, we can use right triangle trig.
We are given the value of ∠A, and side "x" is its adjacent side. We are also given its opposite side, so:
tan (A) = O / A
tan (33) = 25 / x
Solve:
x · tan(33) = 25
x = 38.49 ≈ 38.5
What does 1/8 equal to
Answer:
0.125
Step-by-step explanation:
It could be a lot of things, but if you mean the decimal form then it would be 0.125. Just divide 1 by 8.
Which ordered pair makes both inequalities true? y < 3x – 1 y > –x + 4 On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (0, negative 1) and (1, 2). Everything to the right of the line is shaded. The second solid line has a negative slope and goes through (0, 4) and (4, 0). Everything above the line is shaded.
Answer:
None of the options is true
Step-by-step explanation:
Given
[tex]y < 3x - 1[/tex]
[tex]y > -x + 4[/tex]
Required
Which makes the above inequality true
The missing options are:
[tex](4,0)\ (1,2)\ (0,4)\ (2,1)[/tex]
[tex](a)\ (x,y) = (4,0)[/tex]
Substitute values for x and y in the inequalities
[tex]y < 3x - 1[/tex]
[tex]0<3*4 - 1[/tex]
[tex]0<12 - 1[/tex]
[tex]0<11[/tex] ---- This is true
[tex]y > -x + 4[/tex]
[tex]0 > -4 + 4[/tex]
[tex]0 > 0[/tex] --- This is false
[tex](b)\ (x,y) = (1,2)[/tex]
Substitute values for x and y in the inequalities
[tex]y < 3x - 1[/tex]
[tex]2<3 * 1 - 1[/tex]
[tex]2<3 - 1[/tex]
[tex]2<2[/tex] --- This is false (no need to check the second inequality)
[tex](c)\ (x,y) = (0,4)[/tex]
Substitute values for x and y in the inequalities
[tex]y < 3x - 1[/tex]
[tex]4< 3*0-1[/tex]
[tex]4< 0-1[/tex]
[tex]4<-1[/tex] --- This is false (no need to check the second inequality)
[tex](d)\ (x,y) = (2,1)[/tex]
Substitute values for x and y in the inequalities
[tex]y < 3x - 1[/tex]
[tex]1<3*2-1[/tex]
[tex]1<6-1[/tex]
[tex]1<5[/tex] --- This is true
[tex]y > -x + 4[/tex]
[tex]1 > -2+4[/tex]
[tex]1 > 2[/tex] -- This is false
Hence, none of the options is true
Tele-Mart instituted a 5-for-1 split in April. After the split, Ashlee owned 1,860 shares. How many shares had she owned before the split?
Answer:
372 shares
Step-by-step explanation:
Let
x = shares owned before the split
Share after split : share before split = 5 : 1
Share after split : share before split = 1,860 : x
Equate both ratios
5 : 1 = 1,860 : x
5/1 = 1,860/x
Cross product
5 * x = 1 * 1,860
5x = 1,860
x = 1,860/5
x = 372
x = shares owned before the split = 372 shares
An on-demand movie company charges 52.95 per movie plus a monthly fee of $39.95. Which expression represents
the yearly cost for x movie rentals?
295x+39.95
39.95x295
2958-39 95(12)
295x3995(12)
Hurry I'm being timed !
Answer:
52.95x + 39.95(12)
Step-by-step explanation:
Answer:
52.95 x + 39.95 (12)
Step-by-step explanation:
cost per movie = 52.95
a monthly subscription is 39.95 and there are 12 months in a year so it would be 39.95 x 12
the x would be dependent on the amount of movie rentals and therefore the cost of the rentals = 52.95 x
If 8x−7y=−8 is a true equation, what would be the value of -8+8x−7y?
Answer:
-16
Step-by-step explanation:
-8 + (-8) = -16
Answer:
-16
Step-by-step explanation:
8x−7y=−8
Subtract 8 from each side
-8 +8x−7y=−8-8
-8+8x−7y=−16
