Answer:
9
Step-by-step explanation:
Use Pythagoras’ theorem;
the hypotenuse is 15:
one side that isn't hypotenuse is 12:
[tex]a^2 +12^2=15^2\\= a=225-144\\a=81\\\sqrt{81}=9[/tex]
If you borrow $500 at 6 percent interest for 5 years what is the monthly payment?
Use this model to calculate 3/8 × 2/6 .
A grid is shown with 8 rows and 6 columns. The top 2 rows are colored blue. The left 3 columns are textured. These colors and textures overlap on 6 cells indicated by the first 3 columns of the top two rows.
A. 16 18
B. 13 24
C. 6 48
D. 5 48
The product of numbers is calculated by multiplying them
The result of the product is 6/48
How to multiply the numbersThe product is given as:
3/8 x 2/6
Rewrite properly as:
[tex]\frac 38 * \frac 26[/tex]
Using the model, we have:
[tex]\frac 38 * \frac 26 = 3 * \frac 18 * 2 * \frac 16[/tex]
Rewrite as:
[tex]\frac 38 * \frac 26 = 3* 2 * \frac 18 * \frac 16[/tex]
Multiply the integers
[tex]\frac 38 * \frac 26 = 6 * \frac 18 * \frac 16[/tex]
Multiply the fractions
[tex]\frac 38 * \frac 26 = 6 * \frac 1{48}[/tex]
Multiply the integers and the fractions
[tex]\frac 38 * \frac 26 = \frac 6{48}[/tex]
Hence, the result of the product is 6/48
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Answer:
6/48
Step-by-step explanation:
duhh
Timmy gets 1/3
the profit of
every sale that
he makes, selling
candy. If he
made $45, how
much money did
his sales earn?
Answer:
15
what is 1/3 it's 3 right so $45 is going to be divided by 3 so 45÷3 which is equals to 15
Solve.
[tex]2 5/6 + (-1 4/12) =[/tex]
Answer:
3
Step-by-step explanation:
Answer:
[tex]\frac{25}{6} = 4.16[/tex]
[tex]\frac{-14}{12}=-1.16[/tex]
4.16 + (-1.16)
= 3
Write the expanded form of the expression.
6(3x - 7)
100 points consider the function below -2|x-3|+1 = -2sqrtx-1
Answer:
D. x = 1.7 or x = 5.7
Step-by-step explanation:
The left side of the equation is graphed in blue. The right side of the equation is graphed in red.
The solution of the equation is the x (and y) that make both equations true.
On the graph these solutions are the points where the two graphs intersect.
Those two points have x values that are positive (and y's that are negative) Only answer D. has x-values that correspond to the x-values of the points of intersection.
Answer:
D. x ≈ 1.7 or x ≈ 5.7Step-by-step explanation:
The solution is the x-coordinate of the intersection of the graphs (blue line and red curve).
The points are:
x close to 2 and close to 6Correct choice is D
What is the equation of the line that passes through the points (1, 1) and (7, -5)?
Answer:
y = -1x+2
Step-by-step explanation:
(1,1)(7,-5)
y2-y1/x2-x1 = slope
-5-1/7-1 = -6/6= -1
y-y1 = slope(x-x1) // equation formula
y-1=-1(x-1)
y = -1x + 1 +1
y = -1x+2
Find an equation of the tangent line to y = 2e^x sec(x) at x = pi/4
Answer:
y = 6.20 + 12.4(x - pi/4)
Step-by-step explanation:
dy/dx = 2e^x secx + 2e^x secx * tanx= 2e^x secx (1 + tanx)
At x = pi/4, use sec(pi/4) = [tex]\sqrt{2}[/tex]. tan(pi/4) =1
so dy/dx = 2e^(pi/4) * [tex]\sqrt{2}[/tex] * (1 + 1) = [tex]4 \sqrt{2} e^{\pi/4}[/tex] ≈ 12.4 (This is the slope of the tangent line)
When x = pi/4, y = 2e^(pi/4) * [tex]\sqrt{2}[/tex] = [tex]2 \sqrt{2} e^{\pi/4}[/tex]= 6.20
Then the equation of the tangent line is
y = 6.20 + 12.4(x - pi/4)
A post office sells stamps with 10 different images on them: flowers, trees, insects, birds, landscapes, constellations, frogs, mountains, fish, and bears. The post office has an equal amount of each stamp. One stamp is selected at random. Determine the theoretical probability of selecting a tree or frog stamp. Express your answer as a fraction in simplest form.
Using the it's concept, it is found that the theoretical probability of selecting a tree or frog stamp is of 0.2 = 20%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
A theoretical probability is calculated before experiments.
In this problem:
There is a total of 10 stamps.Of those, 2 have tree or frog stamp.Hence:
[tex]p = \frac{2}{10} = 0.2[/tex]
The theoretical probability of selecting a tree or frog stamp is of 0.2 = 20%.
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A box has 640 nails. Each model boat needs 8 nails to hold it together. How many model boats can be made?
Find the equation of the line parallel to y = 3x - 2 that passes through
the point (4.8) in slope-intercept form.
Answer:
y = 3x - 4
Step-by-step explanation:
a line parallel to another will have the same slope, just a different y-intercept or b-value. Using this, we suggest the equation of the question [tex]y = 3x + b\\[/tex], as we can solve for b. The point (4,8) was given, which means that an input of 4 as x returns 8 as y. Thus, [tex]8 = 3(4) + b[/tex]. Solving this gains b = -4
Khan academy
Please need help
Answer:
-3<x<-2
Step-by-step explanation:
In the graph you can see that from x=-3 to x=-2, the graph is below the x axis, meaning that it is below zero. none of the other options are below zero at their respective ranges, so that's your answer
If A= ("-2" 6 1) (1 9 "-6)" ("-9" 9 "-9)" and B= ("-5" 9 6) (-2 "-7" 4) (1 10 "-1)," find "-4A" + 6B
Jina got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of
ribbon was 21 cents per yard. If after that purchase there was $12.69 left on the card, how many yards of ribbon did Jina buy?
Answer:
the first answer
Step-by-step explanation:
I looked at it
Subtraction is a mathematical operation that reflects the removal of things from a collection. The yards of ribbon that were bought by Jina is 11 yard.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given that Prepaid credit card amount = $15
Also, She bought some bulk ribbon at a craft store and the price of ribbon was 21 cents per yard.
If after that purchase there was $12.69 left on the card.
Now, we can write the following details,
The amount on the credit card = $15
The amount spend on buying the ribbon = $0.21 cents per yard
The amount left on the credit card = $12.69
Further, we can write,
The amount that was used to buy the ribbon
= $15 - $12.69
= $2.31
Now, the length of the ribbon bought by Jina is,
Length of ribbon = $2.31 / $0.21 per yard = 11 yards
Hence, the yards of ribbon that were bought by Jina is 11 yard.
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how to factor x^3 + x - 4 = 0
Answer:
X = 1.378797
Step-by-step explanation:
However, the following root(s) were found by numerical methods.
X = 1.378797
A ream of paper containing 500 sheets is 5 cm thick. How many sheets of this type of paper would there be in a stack 7.5 cm high?
Answer:
The answer is 5.80 cm high
f(x) = -5x^2 + 3x + 2
What is the axis of symmetry?
What's the coordinate of the vertex?
Answer:
axis of symmetry: x = 0.3vertex: (0.3, 2.45)Step-by-step explanation:
For quadratic ax²+bx+c, the axis of symmetry is x=-b/(2a). For your quadratic with a=-5, b=3, the axis of symmetry is ...
x = -(3)/(2(-5))
x = 3/10 . . . . axis of symmetry
__
The coordinates of the vertex are found by evaluating the function at x=3/10.
f(3/10) = (-5(3/10) +3)(3/10) +2 = 1.5(3/10) +2 = 0.45 +2 = 2.45
The vertex is (0.3, 2.45).
I need the answer to this question please.
The value of sin2 Θ is in the 4th quadrant is -24/25
Explanation:
Given the expression of cosΘ= 3/5 with Θ in quadrant 4;
According to SOH, CAH TOA;
cosΘ= adjacent/hypotenuse
Get the opposite
5² = opp² + 3²
opp² = 25 - 9
opp² = 16
opp = 4
SinΘ = opp/hyp
SinΘ = 4/5
Sin2Θ = 2sinΘ cosΘ
Sin2Θ = 2(-4/5)(3/5)
Sin2Θ = -24/25
Hence the value of sin2Θ is in the 4th quadrant is -24/25
What is the measure of the missing angle?
A cannot be determined
B 59 degrees
C 10 degrees
D 121 degrees
Answer:
The angle is 59 degrees.
Step-by-step explanation:
A triangle's angles, in total, must equal 180 degrees.
71 + 50 + (6x-1) = 180
71 +50 = 121
121 + (6x-1) = 180
6x - 1 = 59
Which of the following sets of numbers between 12 and 20 contains only prime numbers .
Answer:
13, 17, 19
Step-by-step explanation:
Go through (12-20) and find the multipliers for each number.
13 = 13 x 1
14 = 7 x 2 , 14 x1 = no
15 = 5 x 3, 15 x 1 = no
17 = 17 x 1
18 = 6 x 3, 9 x 2, 18 x 1 = no
19 = 19 x 1
what is 2x4+1???? please help
Answer:
9
Step-by-step explanation:
1.2x4 =8
2.8+1=9
hope this helped
In the figure below, angles ACB and ANC are right-angles. What is the 10cm area of AABC?
A 24 cm²
B 37.5cm²
C 40cm²
D 75 cm²
Answer:
area of ΔABC = 48 cm²
Step-by-step explanation:
We have been provided with height of 6 cm and have to find base.
using Pythagoras theorem:
a² + b² = c²
a² + 6² = 10²
a² = 100 -36
a² = 64
a = √64
a = 8
Area of both triangles:
[tex]\frac{1}{2}[/tex] * base * height
[tex]\frac{1}{2}[/tex] * 8 * 6
24 cm²
area of both triangles: 24 cm² * 2 = 48 cm²
Apply Pythagorean theorem
[tex]\\ \tt\hookrightarrow AN^2=10^2-6^2[/tex]
[tex]\\ \tt\hookrightarrow AN^2=8^2[/tex]
[tex]\\ \tt\hookrightarrow AN=8cm[/tex]
AB=2(8)=16cmArea
[tex]\\ \tt\hookrightarrow \dfrac{1}{2}bh[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{1}{2}(16)(10)=8(10)=80cm^2[/tex]
Required area:-80/2=40cm^2
(a) 0.893467 rounded to the nearest hundred-thousandth is
Answer
0.89347
.................
Write the whole number as an equivalent fraction with the given denominator.
5= /4
Answer:
20/4
Step-by-step explanation:
5 = x/4
mulitply both sides by 4
x = 20
so the fraction is 20/4
A rectangular corral is enclosed using 120m of fencing. The corral uses the side of a barn as one of its sides, so fencing is required on three sides of the rectangular region. What dimensions would be maximize the area enclosed by the fence?
A. 30m x 60m
B. 10m x 100m
C. 7m x 106m
D. 20m x 80m
Answer: 30m x 60m
The dimensions that would maximize the area enclosed by the fence is 30m × 60m.
Area of a rectangle:area = lwwhere
l = length
w = width
Perimeter of a rectangle:perimeter = 2l + 2wTherefore,
The corral uses the side of a barn as one of its sides, so the fencing is required on three sides of the rectangular region. Therefore,
perimeter = L + 2w
L + 2w = 120
L = 120 - 2w
area = Lw
area = (120 - 2w)w
area = 120w - 2w²
area = -2w² + 120w
We have a quadratic equation and it is parabolic. The leading coefficient is negative. Therefore, the parabola opens downward and the vertex is the maximum point.
The area is maximized at the vertex. Therefore,
To find the vertex, we need to have our quadratic equation in general form,
ax² + bx + c = 0
so a = -2, b = 120
w = -b / 2a
w = - 120 / 2 × -2
w = -120 / -4
w = 30
Therefore,
area = -2(30)² + 120(30)
area = 1800m²
Therefore, the maximum area we can enclose is 1800 m², the width is 30m, then the length will be 60 m because 60 × 30 = 1800 m².
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Find the measure of each acute angle of right triangle ABC with m
Answer:
The value of the angles are 38° and 52° respectively
Let the acute angles be represented by a and b.
Based in the information given,
a = 2(b - 12)
a = 2b - 24.
Note that the angle in an acute angle equals to 90°.
Therefore,
a = 90 - b.
a = 2b - 24
Equate the equations together
90 - b = 2b - 24
2b + b = 90 + 24
3b = 114
b = 114/3
b = 38
Therefore, a will be:
= 90° - 38° = 52°
The value of the angles are 38° and 52° respectively.
Step-by-step explanation:
Answer:
38 52
Step-by-step explanation:
5) Write an equation to demonstrate the subtraction property of equality and solve using the information from this model. 15.4 + x = 23
Answer:
23-15.4= 7.6.
Step-by-step explanation:
All you have to do is subtract
A washer and a dryer cost $1024 combined. The washer cost $74 more than the dryer. What is the cost of the dryer
Answer:
Let the dryer cost x.
Then, the washer costs (x+87)
Together, they cost (x) + (x+87) = 787
2x+87 = 787
2x = 700 [subtract 97 from both sides]
x = 350 [divide both sides by 2]
The dryer cost $350.
Check: The washer cost $437. Together, they cost $787 [good to check, right?]
Step-by-step explanation:
hope it's help!!!
The amount of time it takes Hugo to solve a Rubik's cube is continuous and uniformly distributed between 4 minutes and 11 minutes. What is the probability that it takes Hugo less than 5 minutes given that it takes less than 6 minutes for him to solve a Rubik's cube?
The probability that it takes Hugo less than 5 minutes is 25%.
ProbabilityGiven that the amount of time it takes Hugo to solve a Rubik's cube is continuous and uniformly distributed between 4 minutes and 11 minutes, to determine what is the probability that it takes Hugo less than 5 minutes given that it takes less than 6 minutes for him to solve a Rubik's cube, the following calculation must be performed:
100 / 8 = 12.512.5 x 2 = 25Therefore, the probability that it takes Hugo less than 5 minutes is 25%.
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A university is comparing the grade point averages of theater majors with the grade point averages of history majors. The university currently has 50 total theater majors and 50 total history majors. The mean and standard deviation for each population are shown in the table.
Theater Majors - (Population Mean 3.22 , Population Standard Deviation 0.002)
History Majors - (Population Mean 3.24 , Population Standard Deviation 0.08)
The university wants to test whether there is a significant difference in GPAs for students in the two majors. What is the P-value and conclusion at a significance level of 0.05?
Using the z-distribution, as we have the standard deviation for the population, we have that the correct option is:
The p-value is of 0.0772. Fail to reject the null hypothesis that there is no difference in the GPA's.
What are the hypothesis tested?At the null hypothesis, we test if there is no difference in the means, that is:
[tex]H_0: \mu_T - \mu_H = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is:
[tex]H_1: \mu_T - \mu_H \neq 0[/tex]
What is the distribution of the sampling distribution of sample differences?For each sample, we have that:
[tex]\mu_T = 3.22, s_T = \frac{0.002}{\sqrt{50}} = 0.00028284271[/tex]
[tex]\mu_H = 3.24, s_H = \frac{0.08}{\sqrt{50}} = 0.01131370849[/tex]
Hence:
[tex]\overline{x} = \mu_T - \mu_H = 3.22 - 3.24 = -0.02[/tex]
[tex]s = \sqrt{s_T^2 + s_H^2} = \sqrt{0.00028284271^2 + 0.01131370849^2} = 0.0113[/tex]
What is the test statistic?It is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
[tex]z = \frac{0.02 - 0}{0.0113}[/tex]
[tex]z = -1.77[/tex]
What is the p-value and the decision?Using a z-distribution calculator, considering a two-tailed test, as we are testing if the mean is different of a value, with z = -1.77, it is found that the p-value is of 0.0772.
Since the p-value is greater than the significance level of 0.05, the correct option is:
The p-value is of 0.0772. Fail to reject the null hypothesis that there is no difference in the GPA's.
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Answer:
The P-value is 0.0772. Fail to reject the null hypothesis that there is no difference in the GPAs.