Step-by-step explanation:
[tex]\angle 3[/tex] and [tex]\angle 16[/tex] are alternate exterior angles so they are equal to each other, which means
[tex]5x - 30 = 3x + 10 \Rightarrow x = 20[/tex]
Solving for the measure of [tex]\angle 16[/tex], we get
[tex]m\angle 16 = 5(20) - 30 = 70°[/tex]
Since [tex]\angle 12[/tex] and [tex]\angle 16[/tex] are supplementary,
[tex]m\angle 12 = 180° - 70° = 110°[/tex]
Answer:
ur image wont load
Step-by-step explanation:
Help please guys thanks
We know that [tex]a^{m/n}=\sqrt[n]{a^m}[/tex],
so in your case,
[tex](-8)^{2/3}=\sqrt[3]{(-8)^2}=\sqrt[3]{64}=\boxed{4}[/tex]
Hope this helps :)
What is the slope of the line that contains these points?
х
-1
0
1
2
y
10
18
26
34
slope:
Answer:
8.
Step-by-step explanation:
The slope =
difference in y coordinates of 2 points / difference in coordinates of corresponding x coordinates.
So taking the first 2 points:
The slope = (18-10) / 0 - (-1)
= 8/1
= 8.
This is confirmed by slope between the second and third points
slope = 26-18/ (1-0) = 8.
Sally went diving. She descends 2 feet every second. After 4 seconds, how many feet
has she descended?
Answer:
8 feet
Step-by-step explanation:
You can simply do 2×4=8
or
1 second = 2 feet
2 second= 4 feet
3 second =6 feet
4 second =8 feet
Brainliest please~
8 feet
For every 2 feet = 1 second
Therefore for 4 seconds
= ( 2 × 4 )/ 1
= 8ft
see the image too
Certify Completion Icon Tries remaining:2 A town recently dismissed 10 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random, what is the probability that exactly 5 employees were over 50
Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
7 + 18 = 25 employees, which means that [tex]N = 25[/tex]
7 over 50, which means that [tex]k = 7[/tex]
10 dismissed, which means that [tex]n = 10[/tex]
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]
0.055 = 5.5% probability that exactly 5 employees were over 50.
help !!!! what’s the solution
The ratio of the side lengths of Rectangle A to Rectangle B is 3 to 7. What is the
ratio of their areas?
9514 1404 393
Answer:
9 : 49
Step-by-step explanation:
Assuming the rectangles are similar, the ratio of their areas is the square of the ratio of their side lengths.
sides ratio = 3 : 7
areas ratio = 3² : 7² = 9 : 49
Match each shape to the number of lines of reflection that will reflect the shape onto itself. Drag the items on the left to the correct location on the right.
Answer:
rectangle- 2 lines of reflection
trapezoid- 0 lines of reflection
regular pentagon- 5 lines of reflection
square- 4 lines of reflection
Step-by-step explanation:
⅗ Write the numerator and denominator of each of the following rational numbers
Answer:
1 3 5 7 9 11
Step-by-step explanation:
same like this do the question the answer will come
write the equation of a line of a line passing through the points (3,1) and (6,3).
Answer:
i think its 2 1
Step-by-step explanation:
Answer:
y =2/3x-1
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( 3-1)/ (6-3)
= 2/3
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2/3x +b
Using a point
3 = 2/3(6)+b
3 = 4+b
3-4 =b
-1=b
y =2/3x-1
Answer by any chance?❤️
Step-by-step explanation:
Question 2.[tex] \frac{ \frac{6}{7} }{ \frac{9}{14} } [/tex]
[tex] = \frac{6}{7} \times \frac{14}{9} [/tex]
[tex] = \frac{2}{1} \times \frac{2}{3} [/tex]
[tex] = \frac{4}{3} = 1 \frac{1}{3} (Ans) [/tex]
Question 3.[tex] \frac{18}{x} = \frac{6}{10} [/tex]
[By cross multiplication]
=> 18 × 10 = 6 × x
[tex] = > \frac{18 \times 10}{6} = x[/tex]
=> 3 × 10 = x
=> x = 30 (Ans)
Plz I need help on this question
Answer:
11.33
Step-by-step explanation:
First find the markup
8.80 * 25%
8.8 *.25 = 2.20
The new price is 8.80+2.20 = 11
Now find the tax
11*.03
.33
Add the tax to the new price
11+.33
11.33
Answer:
$11.33
Step-by-step explanation:
First divide 25% by 100, 0.25.
Then multiply 8.80 x 0.25 = 11.
Again, divide 3% by 100, 0.03
Then finally take 11.00 and multiply it with 0.03.
11.00 x 0.03=
$11.33
Given the similarity statement ΔJKL∼ΔNOP , what’s the corresponding angle of ∠J
9514 1404 393
Answer:
∠N
Step-by-step explanation:
J is the first letter listed in the left side of the similarity statement. The corresponding angle is the first letter listed in the right side of the similarity statement: ∠N.
__
Corresponding angles are listed in the same order. The similarity statement means ...
∠J≅∠N
∠K≅∠O
∠L≅∠P
Answer:
<J = <N
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
Can someone please help me with this problem? I tried inputting the numbers into the standard deviation equation but I did not get the right answer. Can someone please help me? Thank you for your time.
Answer:
97.8
Step-by-step explanation:
add together 97.3 +0.5
An electronics company wants to compare the quality of their cell phones to the cell phones from three of their competitors. They sample 10 phones from each of the four companies and count the number of defects for each phone. If ANOVA was used to compare the average number of defects, then the treatments would be defined as: ______.
Answer:
The treatment should be stated by the four companies,since it more interested in the quality among each of the companies to be compared.
Step-by-step explanation:
The mean number of hours of study time per week for a sample of 562 students is 23. If the margin of error for the population mean with a 98% confidence interval is 2.1, construct a 98% confidence interval for the mean number of hours of study time per week for all students.
Answer:
The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).
Step-by-step explanation:
Confidence interval:
Sample mean plus/minus the margin of error.
In this question:
Mean of 23.
Margin of error 2.1.
Then
23 - 2.1 = 20.9
23 + 2.1 = 25.1
The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).
Surds see attached 20 points
Answer:
[tex]5\sqrt{2} \\45[/tex]
Step-by-step explanation:
just multiply
Answer:
a) 5√2
b) 135
Step-by-step explanation:
√5·√10 is equivalent to √50, which in turn is equivalent to √25·√2, or 5√2.
√27·√75 can be simplified by factoring:
√3·√9·√3√25, or (because √3·√3 = 3):
(3)(9)(5) = 135
Question 4 of 10
What else would need to be congruent to show that ABC= AXYZ by SAS?
Answer:
D
Step-by-step explanation:
The correct answer is D. Answered by Gauthmath
The angles in a triangle are represented by x, x+10, and x+50. What is the measure of the largest angle?
A.70 degrees
B.80 degrees
C.100 degrees
D.90 degrees
Given that,
The angles in a triangle are represented by x, x+10, and x+50.
We had to,
find the measure of the largest angle.
Let's start to solve,
→ x + (x+10) + (x+50) = 180°
→ x + x + x = 180° (-50 -10)
→ 3x = 180° -60
→ 3x = 120
→ x = 120/3
→ x = 40°
Then the value of x + 10,
→ x + 10
→ 40 + 10
→ 50°
Then the value of x + 50,
→ x + 50
→ 40 + 50
→ 90°
The measure of the largest angle is,
→ D. 90 degrees
Hence, option (D) is correct answer.
Step-by-step explanation:
good of you and good workings
Find an equation of the line that is the perpendicular bisector of the line segment joining the points (6,2) and (18,6)
Answer:
y= -3x +40
Step-by-step explanation:
Properties of perpendicular bisector:
• perpendicular to the given line
• cuts through the center of the given line
The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.
Let's find the gradient of the given line first.
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Gradient of given line
[tex] = \frac{6 - 2}{18 - 6} [/tex]
[tex] = \frac{4}{12} [/tex]
[tex] = \frac{1}{3} [/tex]
The product of the gradients of perpendicular lines is -1.
m(⅓)= -1
m= -1(3)
m= -3
Substitute m= -3 into the equation:
y= -3x +c
To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.
[tex]\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}[/tex]
Midpoint
[tex] = ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )[/tex]
[tex] = ( \frac{24}{2} , \frac{8}{2} )[/tex]
[tex] = (12,4)[/tex]
y= -3x +c
when x= 12, y= 4,
4= -3(12) +c
4= -36 +c
c= 4 +36
c= 40
Thus, the equation of the perpendicular bisector is y= -3x +40.
degree and classification of 4x^2+32x+63?
nvm its quadratic trinomial
Answer:
Pertaining to the mathematical expression conveyed, the answer to such proposed interrogate is acknowledged as the following:
Degree: 2nd degree term.
Classification: Quadratic trionomial.
Step-by-step explanation:
Evaluating the Degree:
The degree is acknowledged as the predominating term adjacent to a base of a peculiar value that denotes the particular allocation within a polynomial.
4x^2 has the highest degree of 2.
32x has the degree of one, being that x individually is x^1.
Since polynomials are defined by the term in which obtains the greatest degree, ^2 is referred to as quadratic, whereas ^3 is cubic, ^4…
Classification Evaluation:
Such could be determined by evaluating for the quantity of terms present within the mathematical expression or statement.
4x^2 is the first term.
32x is the second term.
63 is the third term (considered a constant).
Thus, the correct answer is a quadratic trinomial.
*I hope this helps.
Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.)
[tex] \sqrt[3 ]{28} [/tex]
Answer:
Mix fraction: 3 1/27
Improper fraction: 82/27
Decimal approximation: 3.037
Step-by-step explanation:
What value is close to 28 that is a perfect cube...27 which equals 3^3.
So let's find the tangent line to the curve y=cubert(x) at x=27.
We will use this equation to approximate what happens at x=28.
First let's rewrite the radical in our equation;
y=x^(1/3)
Now differentiate
y'=(1/3) x^(1/3-1) by power rule
Simplify
y'=(1/3) x^(-2/3) or (1)/(3x^[2/3])
So the slope of our tangent line at x=27 is (1)/(3(27)^[2/3])=1/(3(3)^2)=1/(3×9)=1/27.
We will also need a point on this tangent line....We know we have the point at x=27 because that is what our tangent line to curve is being found at.
So at x=27, we have y=cubert(27)=3. We used our equation y=cubert(x) here.
So we want to find the equation of the line that contains point (27,3) and has slope 1/27.
Point-slope form is
y-y1=m(x-x1)
Plug in our values
y-3=(1/27)(x-27)
Add 3 on both sides
y=3+(1/27)(x-27)
We will use this linear equation to approximate cubert(28) by replacing x with 28.
y=3+(1/27)(28-27)
y=3+(1/27)(1)
y=3+1/27
You can write that as a mix fraction if you want.
This value is than 3 but super close to 3 since 1/27 is close to 0.
Mix fraction: 3 1/27
Improper fraction: 82/27
Decimal approximation: 3.037
Cubert of 28 when smashed into calculator as is gives approximately 3.0366 which is pretty close to our approximation.
Using a linear approximation method f'(29) ≈ 3.1465.
What is linear approximation method?
A linear approximation is an approximation of a general function using a linear function (specifically, an affine function). They are widely used in the finite difference method to establish first-order methods to solve or approximate the solutions of equations.
Linear approximation, or linearization, is a method by which we can approximate the value of a function at a certain point. The reason linear approximation is useful is that finding the value of a function at a particular point can be difficult. Square roots are a good example of this.
Linear approximated as:
f(x+Δx)≈f (x)+Δx x[tex]f^{'}[/tex](x)
Take x = 28 and Δx = 1
f(x) = [tex]\sqrt[3]{x}[/tex]
Substitute 28for x
f(x) = [tex]\sqrt[3]{28}[/tex]
f(x) = 3.0365
So, we have
f(x+Δx)≈f (x)+Δx x[tex]f^{'}[/tex](x)
f(28+1)≈3.0365+1.[tex]f^{'}[/tex](x)
f(29)≈3.0365+1.[tex]f^{'}[/tex](x)
To calculate f'(x)
We have
f(x)=[tex]\sqrt[3]{x}[/tex]
Rewrite as
f(x)= [tex]x^{\frac{1}{3} }[/tex]
Differentiate
[tex]f^{'}[/tex]= [tex]\frac{1}{3}[/tex][tex]X^{\frac{1}{3}-1 }[/tex]
f' = [tex]\frac{1}{3}[/tex] . [tex]\frac{x^{\frac{1}{3} } }{3x}[/tex]
f'(29) = [tex]\frac{29^{\frac{1}{3} } }{3\times29}[/tex]
f'(29) =9.66/87
f'(29) = 3.22/29
f'(29) ≈ 3.0365+1x 3.22/29
f'(29) ≈3.0365+ 0.1110
f'(29) ≈ 3.1465
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A zookeeper perdiceted that the wight of a newborn lion would be 2.8 pounds when the zoo’s lion gave birth ,the newbor. Weight 3.5 pounds what is the zookeeper’s percent error ? Round to nerds err percent
Answer:
20%
Step-by-step explanation:
3.5 - 2.8 = 0.7
0.7 ÷ 3.5 = 0.2
0.2 × 100 = 20
The answer is 20%.
Hope this helped.
Answer:
predicted wight=2.8
Actual wight = 3.5 pounds
(3.5-2.8)/3.5
=0.7/3.5 × 100
=100/5=20%
Answer: 20%
OAmalOHopeO
What is y-3=3/4(x-5) in standard form?
Answer:
[tex]y-3=\frac{3}{4} (x-5)\\\\y-3=\frac{3}{4}x-\frac{3}{4}(5)\\\\y=\frac{3}{4} x+3-\frac{15}{4} \\\\y=\frac{3}{4} x+\frac{12}{4} -\frac{15}{4} \\\\y=\frac{3}{4} x-\frac{3}{4}[/tex]
Is this standard form? :\
Answer:
3x-4y=3
Step-by-step explanation:
Hi there!
We are given the equation y-3=[tex]\frac{3}{4}(x-5)[/tex], and we want to write it in standard form
Standard form is given as ax+by=c, where a, b, and c are integer coefficients, a CANNOT be 0 and CANNOT be negative, and b also CANNOT be 0
So let's expand the parentheses in the equation
Do the distributive property
y-3=[tex]\frac{3}{4}x-\frac{15}{4}[/tex]
Add 3 to both sides
y=[tex]\frac{3}{4}x-\frac{3}{4}[/tex]
We expanded the parentheses, but the equation is now in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
Remember that we want it in standard form, which is ax+by=c
Subtract [tex]\frac{3}{4}x[/tex] from both sides
[tex]\frac{-3}{4}x+y=\frac{-3}{4}[/tex]
Remember that the coefficients of a, b, and c need to be integers, and also that a (the coefficient in front of x) CANNOT be negative
So multiply both sides by -4
[tex]-4(\frac{-3}{4}x+y)=-4(\frac{-3}{4})[/tex]
Distribute -4 to every number
[tex]-4(\frac{-3}{4}x)+-4(y)=-4(\frac{-3}{4})[/tex]
Multiply
[tex]\frac{12}{4}x-4y=\frac{12}{4}[/tex]
Simplify
3x-4y=3
There's the equation in standard form
Hope this helps!
pleaseee i need help!
2 questions in one pleasee 90 points!
Answer:
A the answer is A if you look at it .
Answer:
The first one is B) point D
The second one is D) (0,0)
Hope this helps!
btw, coordinates are in (x,y) form, so the other answer above me is wrong.
The x - intercept of the function f(x) = x2 + 4x - 12 is:
A) (-4,0)(3,0)
B) (-2,0)(6,0)
C) (-6,0)(2,0)
D)(4,0)(-3,0)
PLEAEE HELP ITS REALLY URGENT AND WILL MARK AS BRAINLIEST!!!
Answer:
C) (-6,0)(2,0)
For x-intercept, f(x) = 0:
[tex]{ \tt{ {x}^{2} + 4x - 12 = 0 }} \\ { \tt{(x - 2)(x + 6) = 0}} [/tex]
Answer:
C) (-6,0)(2,0)
Step-by-step explanation:
f(x)= x²+4x-12
(x-2)(x+6)=0
x=2
x=-6
I need help with this
Answer:
D
Step-by-step explanation:
The table gives us the squares of certain values, and can be used to find the square root of certain values as well. For example, if 6² = 36, we can say that √36 = 6. Given this information, we can say that √47.6 is 6.9, and √49 = 7. If we look at the square root graph (√x=y), we can see that as x goes up, y goes up, and when x goes down, y goes down.
Therefore, we can say that the square root of 48 is between 6.9 and 7. We don't know exactly where it is, as there is no formula given to find it, so what Gina can do is go through the values between 6.9 and 7.0 and look for √48
Find z such that 4.8% of the standard normal curve lies to the left of z. (Round your answer to two decimal places)
Answer:
The correct answer will be "-1.66".
Step-by-step explanation:
Let z₀ be,
[tex]P(z<z_0)=4.8 \ percent[/tex]
[tex]=0.048[/tex]
⇒ [tex]\Phi (z_0)=0.048[/tex]
Now,
⇒ [tex]\Phi (-1.6646)=0.048[/tex]
[tex]z_0=-1.6646[/tex]
[tex]\simeq -1.66[/tex]
Thus the above is the right answer.
What relationship do the ratios of sin x° and cos y° share? A right triangle is shown with one leg measuring 12 and another leg measuring 5.
Find the number of terms, n, of the arithmetic series given a1=11, an=95, and Sn=689.
A. 16
B. 15
C. 13
D. 14
Answer:
13
Step-by-step explanation:
Its calculate the common difference first.
(95-11)/(n-1).
We also have the sum of these n terms is 689.
So we have the following:
11
+(11+(95-11)/(n-1))
+(11+2(95-11)/(n-1))
+...
+(11+(n-1)(95-11)/(n-1))
This can be re-expressed alittle:
There are (n) amount of 11's in the addition... also 1+2+3+...+(n-1)=(n-1)(n)/2.
So we have the sum is
11(n)+n(n-1)/2×(95-11)/(n-1)
But this equal to 689.
We need to solve the following equation:
11(n)+n(n-1)/2×(95-11)/(n-1)=689
The (n-1)'s in second term can cancel.
11(n)+n/2×84=689
11n+42n=689
53n=689
53n=689
n=689/53
n=13
The number of the terms for the arithmetic series is 13.
What is arithematic seies?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
The formula for calculating the sum of the arithmetic progression.
Sn = ( n / 2 ) [ a₁ + a[tex]_{n}[/tex]]
689 = ( n / 2 ) [ 11 + 95 ]
689 x 2 = n x 106
n = 1378 / 106
n = 13
Therefore, the number of terms for the arithmetic series is 13.
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Which of the following phrases should not be expressed using a negative number?
Answer:
its 1900 Bc. Because BC stand for before chirst
Step-by-step explanation: