The simplified expression is [tex]y^{\frac{7}{2} }[/tex]
How is the given expression simplified?
[tex]6\sqrt{y^{21} } \\\\= [(y)^{21} ]^{\frac{1}{6} } \\\\[/tex]
By applying power rule of exponents ,
[tex]6\sqrt{y^{21} } =[/tex] [tex]y^{\frac{7}{2} }[/tex]
What is power rule of exponents?
The exponent power rule is [tex](a^{m} )^{n} = a^{mn}[/tex]Exponent times power is how you raise a number with an exponent to a power.When a base is raised to a power and then the entire expression is raised to another power.An algebraic expression can be made simpler by using the power of a power rule in exponents.To learn more about power rule, refer:
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The abbreviated form is
How is the expression that is given simplified?
by using the exponents' power rule.
What is the exponents power rule?
Exponent power rule states that
You increase a number with an exponent to a power by multiplying the exponent by the power.when the expression as a whole is raised to a higher power after raising a base to that powerThe power of a power rule in exponents can be used to simplify an algebraic expression.To learn more about power rule refer to:
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. how many 1/4s are in 6
Let us divide 6 by 1/4
6/1 ÷ (1/4)
6/1*4/1 (Turning the second fraction upside down and multiplying it by the first fraction)
24 (Multiplying)
The answer is 24.
Answer:
Step-by-step explanation:
Since there are four 1/4 in 1 then you have to multiple 6*4= 24!
log (5x +9)= 1+ log (x - 5)
çok acill çözüm lütfeen
Answer: it is yes
Step-by-step explanation:
When the crate folow top botom nuberto
If it takes Carlos 15 weeks to make 3 birdhouses, how long will it take him to make 11 birdhouses?
Applying proportion
we have that
15 weeks/ 3 birdhouses=x/11 birdhouses
solve for x
x=(15/3)*11
x=5*11
x=55 weekshelp me please
thank you
Answer:
Domain: A, [tex)(-\infty, \infty)[/tex]
Range: [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
According to government data, the probability that an adult was never in a museum is 13%.
We need to find the mean and the standard deviation with the next information:
- 30 adults were surveyed
-The probability that an adult was never in a museum is 13%.
To find the mean:
30 adults *0.13 probability that an adult was never in a museum
= 3.9
SET A
15 points
Hi to everyone I just need an answer for my activity one of my subject
thank you:)
Answer:
8 points for solving 6 questions?? Nah thats worth 25 points
Step-by-step explanation:
Find the equation of a line with given slope and containing given point. Write the equation in sole-intercept m= -7/2, point (-8,-4)
Given:
There are given that the slope and the point:
[tex]\begin{gathered} m=-\frac{7}{2} \\ point:\left(-8,-4\right) \end{gathered}[/tex]Explanation:
To find the equation, first, we need to see the formula for slope-intercept form:
So,
From the slope-intercept formula;
[tex]y=mx+b[/tex]Where,
[tex]\begin{gathered} m=-\frac{7}{2} \\ \lparen x,y)=\left(-8,-4\right) \end{gathered}[/tex]Now,
We need to find the value of b by using given information:
So,
Put all the given values into the given slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ -4=-\frac{7}{2}\left(-8\right)+b \\ -4=28+b \\ b=-32 \end{gathered}[/tex]Then,
Put the value of b and m into the slope-intercept form;
So,
[tex]\begin{gathered} y=mx+b \\ y=-\frac{7}{2}x+\left(-32\right) \\ y=-\frac{7}{2}x-32 \end{gathered}[/tex]Final answer:
Hence, the equation of a line is shown below;
[tex]y=-\frac{7}{2}x-32[/tex](a) Latoya's test score average Increased by 8 points this semester.Write a signed number to represent this change in average.(b) Isabel lost 70 dollars from her pocket.Write a signed number to represent this change.
Solution
a) Latoya's test score average Increased by 8 points this semester.
This simply means there is an increase of 8 points in Latoya's test score average.
Thus, a signed number that represents this change in average is +8 points
b) Isabel lost 70 dollars from her pocket.
This simply means there is a decrease in the money in Isabel's pocket.
Thus, a signed number to represent this change is -70 dollars
The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 91 square centimeters?
____ cm/min
which of the following polynomials is in standard form?y^12-y^15+y^10-4yz^5+z^3-z^2-42z^3+z^5-9x+x^2+x^3+x^4
For a polynomial to be in standard form, the terms are arranged from the highest exponent to the lowest exponent.
Thus, from the polynomials given, the polynomial in standard form is:
[tex]z^5+z^3-z^2-4[/tex]This is because the term with the highest exponent is the first term, the next exponent is 3, followed by the term with an exponent of 2, then the last term is the term with the least exponent.
ANSWER:
[tex]z^5+z^3-z^2-4[/tex]Find the length of strapping (in inches) needed to attach a pipe to the wall. Assume the wall is at a right angle and the straps connect to the wall at right angles.
The length of strapping (in inches) needed to attach a pipe to the wall. Assume the wall is at a right angle and the straps connect to the wall at right angles is 31.77 in.
Length of strappingGiven :
Length = 16.00 in diameter pipe
Now let determine or find the Length since the diameter pipe is 16.00 in.
Length :
Length = 1.10 ×2 + 16.00 /2 × 2 + 1 /4 π · 16.00
Length = 3.20 + 16.00 + 4π
Length = 19.20 + 4π
Length = 31.766
Length = 31.77 inches (Approximately)
Therefore the length is 31.77 inches.
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Find the length of the diameter of the circle
with the following equation: (x-4)^2+(y-2)^2=5
The length of the diameter of the circle is found as the 2×(√5).
What is termed as the equation of the circle?The equation of circle offers an algebraic method for describing a circle given its center and radius length. The equation of a circle differs from the formulas used to calculate a circle's area or circumference. The standard equation for a circle with a radius r and a center at (x1,y1) is: (x−x1)²+(y−y1)²=r².,
For the given question;
The equation of the circle is given as;
(x-4)^2+(y-2)^2=5
Comparing the equation of the circle with the standard form.
Radius r² = 5
Then, r = √5
Now, the diameter is the twice of the radius.
Diameter = 2×radius
Diameter = 2×(√5)
Thus, the length of the diameter of the circle is found as the 2×(√5).
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Which of the following side lengths would create a right triangle? Select all
that apply.
5, 5, 10
3,4,7
12, 16, 20
4.5, 6, 7.5
11, 60, 61
6,9, 10
3, 4, 12
8, 15, 17
Answer:
5,12,13
Step-by-step explanation:
first you write out a^2 or a squares + b^2=C ^2 You plug in for a and b the smaller numbers then for c you put the biggest number. Now square everything. And you should get 25 for a. 144 for b. 169 for c. Now add a and b which is25+144 and that equals 169. So 5,12,13 is your answer.
A family creates a monthly budget based on their combined wages and expenses for one month. Complete the budget by choosing the correct option for each cell labeled A through E.
Budgeted Income $ Actual Income $ Difference
Wages $2,500.00 Wages $2,650.00 $150.00
Total Budgeted Wages $2,500.00 Total Actual Income $2,650.00 $150.00
Budgeted Expenses $ Actual Expenses $ Difference
Food $525.00 Food $500.00
A.
Credit Card $100.00 Credit Card $100.00 $0.00
Field Trips $0.00 Field Trips $15.00 -$15.00
Gas $150.00 Gas $120.00 $30.00
Clothing $0.00 Clothing $80.00
B.
Gifts $100.00 Gifts $20.00 $80.00
Entertainment $100.00 Entertainment $65.00
C.
Mortgage Payment $1,080.00 Mortgage Payment $1,080.00 $0.00
Utility Bills $160.00 Utility Bills $140.00 $20.00
Car Payment $225.00 Car Payment $225.00 $0.00
Car Insurance $157.00 Car Insurance $157.00 $0.00
Total Budgeted Expenses $2,597.00 Total Actual Expenses $2,502.00 $95.00
Surplus/Shortage D. Surplus/Shortage E. $245.00
$
$
$
$
$
Step-by-step explanation:
A. 525 - 500 = 25
B. 0 - 80 = -80
C. 100 - 65 = 35
D. 2,500 - 2,597 = 97 shortage
so: -97
E. 2,650 - 2,502 = 148 surplus
so: 148
Factorise fully the following
9x^2+3x^3
Answer:
[tex]3x^2\left(3+x\right)[/tex]
Step-by-step explanation:
Look for common factor: [tex]3x^{2}[/tex] since we take the least exponent
and between numbers (3,9) the common factor is 3.
Thefore, we need to divide [tex]3x^2[/tex] by the equation.
[tex]3x^2(3+x)[/tex].
Step-by-step explanation:1. Write the expression.[tex]9x^2+3x^3[/tex]
2. Find a common denominator for both expressions, based on the x variable.[tex]\frac{9x^2}{3x^2} +\frac{3x^3}{3x^2} \\ \\3x^2(3+x)[/tex]
3. Express your result.[tex]9x^2+3x^3=3x^2(3+x)[/tex].
Write an equation of the line with the given slope and containing the given point. Write the equation in the form y = mx + b.
Slope -4; through (-3, -6)
Group of answer choices
y = -4x - 18
y = -4x + 18
y + 6 = x + 3
Answer:
y = -4x - 18
Step-by-step explanation:
Slope: -4; (-3, -6)
(x₁, y₁)
y - y₁ = m (x - x₁)
y - (-6) = -4 (x - (-3)
y + 6 = -4 (x + 3)
y + 6 = -4x - 12
-6 -6
------------------------
y = -4x - 18
I hope this helps!
a multiple-choice test has 5 questions, each with 4 choices for the answer and assume only one of the choices is correct. What is the probability you get at least one question correctly?
The probability that you will get at least one question correctly is 3/4
How to calculate the probability of getting at least one question correctly?Given that the test has 5 questions and 4 choices per question. Therefore:
Total number choices = 5 x 4 = 20 choices
If you are to get at least one question correctly. That means you can either get 1, 2, 3, 4 or 5 questions correctly. Therefore, the probability of getting at least one question correctly will be the sum of the probability of getting 1, 2, 3, 4 or 5 questions correctly:
Note: there are only 5 correct answers and 20 choices
P(1 correct) = 1/20, P(2 correct) = 2/20 = 1/10, P(3 correct) = 3/20, P(4 correct) = 4/20 = 1/5 and P(5 correct) = 5/20 = 1/4
P(at least one question correctly) = P(1 correct) + P(2 correct) + P(3 correct) + P(4 correct) + P(5 correct)
P(at least one question correctly) = 1/20 + 1/10 + 3/20 + 1/5 + 1/4 = 3/4
Therefore, the probability of you getting at least one question correctly is 3/4
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Match the pairs of angles formed by the parallel lines and transversal to their correct vocabulary identification
The angles that are formed by the parallel lines and the transversal are:
1. Vertical Angles
2. Same-side Exterior Angles
3. Corresponding Angles
4. Alternate Interior Angles
5. Alternate Exterior Angles
6. Same-side Interior Angles
7. Adjacent Angles
What are Special Angle Pairs that are Formed by Parallel Lines and Transversal?The following are special angle pairs that are formed when a transversal intercepts two parallel lines:
1. Vertical Angles: These are nonadjacent angles that share the same vertex and are directly opposite each other. An example of such angle pair is angle 6 and angle 7.
2. Same-side Exterior Angles: These are exterior angles that lie on the same side of a transversal but on sperate parallel lines. Example include angle 2 and angle 8.
3. Corresponding Angles: These angles are located on each parallels lines that are cut across by a transversal and lie relatively in the same corner to each other. An example is, angle 1 and angle 5.
4. Alternate Interior Angles: an example of such pair of interior angles that lie on opposite side of a transversal is, angle 3 and angle 6.
5. Alternate Exterior Angles: An example of a pair of alternate exterior angle is angle 2 and 7.
6. Same-side Interior Angles: These pair of angles are interior angles on the same side of a transversal. Example of such pair of angles is, angle 4 and angle 6.
7. Adjacent Angles: These are angles that share a common side and a vertex, an example is: angle 1 and angle 2.
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Find the surface area of the rectangular prism.4 yd3 yd3 yd
Surface area of rectangular prism,is'
A=2(wl+hl+hw)
h-height
l-length
w-width
A=2(3X3 + 4X3 + 4X3)
A=66 Sq units
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither. 2. A(0,2), B(5, 4), C(1.8).D(3,3)m(TABm(CD)Types of Lines
A (0,2) B (5,4)
C(1,8) D( 3,3)
Apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]For AB
[tex]m=\frac{4-2}{5-0}=\frac{2}{5}[/tex]For CD
[tex]m=\frac{3-8}{3-1}=-\frac{5}{2}[/tex]So both slopes are negative reciprocals of each other.
They are perpendicular lines.
i have to solve for x and i dont know how to
The value of x is 9.
Given:
The length of the tangent lines are given as, 5x and 7x-18.
The objective is to find the value of x.
The two tangents of a circle drawn from a point outside a circle will always be equal.
Then, the value of x can be solved by,
[tex]\begin{gathered} 5x=7x-18 \\ 5x-7x=-18 \\ -2x=-18 \\ x=-\frac{18}{-2} \\ x=9 \end{gathered}[/tex]Hence, the value of x is 9.
QUESTION 3 Round the following to the most appropriate whole number. The ratio of children to adults at an amusement park is typically 5 to 3. 201 adults are in the park. How many children should be in the park?
335 children should be in the park, if the ratio of children to adults at an amusement park is typically 5 to 3 and 201 adults are in the park.
What is ratio?A ratio is the comparison of two similar quantities or the proportion of one similar quantity to another. With the same meaning, ratios can be expressed in three different ways using words or symbols. In other words, ratios can be expressed by sandwiching a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.
The ratio of ninth-graders to tenth-graders can take on any of the three forms listed below, using the previous example of comparing the two groups of students in Ms. Jones' class:
10 /20
10 to 20
10 : 20
Given ratio of children to adults is 5:3
5 + 3 = 8
5/8 are children and 3/8 are adults
Let the total no. of people be x
3/8 = 201/x
x = 201 × 8/3
= 536
Now. no. of children is
5/8 × 536
= 335
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Find the radius of the piñata in feet. near to nearest hundredth.
Explanation:
The formula is given below as
[tex]\begin{gathered} S=4\pi r^2 \\ where, \\ S=surfacearea=60ft^2 \\ r=radius \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} S=4\pi r^{2} \\ 60=4\pi r^2 \\ r^2=\frac{60}{4\pi} \\ r^2=\frac{15}{\pi} \\ square\text{ root both sides } \\ r=\sqrt{\frac{15}{\pi}} \\ r=2.19 \end{gathered}[/tex]Hence,
The final answer to the nearest hundredth is
[tex]2.19[/tex]Classify the following polynomials as: Constant MonomialLinear MonomialQuadratic MonomialCubic MonomialFourth Degree MonomialLinear BinomialQuadratic BinomialCubic BinomialQuadratic TrinomialFourth Degree BinomialFifth Degree Monomial
Solution:
Given the expressions;
[tex]\begin{gathered} -11z \\ -23 \\ 9x^4+9 \\ 2h^2-1,000 \end{gathered}[/tex]A linear monomial is a polynomial whose degree is one and has one terms.
A constant monomial is a term with only a number.
A fourth degree binomial is a polynomial whose degree is 4 and has two terms.
A quadratic binomial is a polynomial whose degree is 2 and has two terms.
ANSWERS:
[tex]\begin{gathered} -11z\ldots\ldots\ldots.....\ldots\ldots....\text{ Linear monomial} \\ -23\ldots\ldots\ldots.....\ldots..\ldots...Cons\tan t\text{ monomial} \\ 9x^4+9\ldots\ldots\ldots.....\ldots\text{.. Fourth degree binomial} \\ 2h^2-1,000\ldots.\ldots..\ldots..\ldots..Q\text{uadratic binomial} \end{gathered}[/tex]Statistics questions pictured in attachment.
Using the normal distribution, it is found that:
a) The variable used in this problem is: The time (in hours) a 4-year old spends unsupervised per day.
b) The distribution is: X ~ N(3, 1.8).
c) The probability is P(X < 1) = 0.1335, and is given by the bottom left graph.
d) The percentage of children who spend over 10 hours a day unsupervised is of 0.01%.
e) 90% of the children spend at least 0.7 hours unsupervised.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.The variable used in this problem is:
The time (in hours) a 4-year old spends unsupervised per day, as the distribution involves only 4-year old children, and the mean and the standard deviation are measured in hours.
The mean and the standard deviation of the distribution are given, respectively, by:
[tex]\mu = 3, \sigma = 1.8[/tex].
Hence the distribution can be described approximately as follows:
X ~ N(3, 1.8).
The probability that a person spends less than 1 hour a day unsupervised is the p-value of Z when X = 1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1 - 3)/1.8
Z = -1.11
Z = -1.11 has a p-value of 0.1335.
The bottom left graph shows this probability, as the number in hours cannot be less than 0(there is no negative number of hours).
The proportion of children who spends over 10 hours a day unsupervised is one subtracted by the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (10 - 3)/1.8
Z = 3.89
Z = 3.89 has a p-value of 0.9999
1 - 0.9999 = 0.0001, hence the percentage is of 0.01%.
For item e, the measure is the 10th percentile, which is X when Z = -1.28, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-1.28 = (X - 3)/1.8
X - 3 = -1.28 x 1.8
X = 0.7 hours.
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481,462 rounded to the nearest hundred thousand
Answer: 500,000
Step-by-step explanation: To round the numbers their nearest hundred thousand, first we have to make the first five digits into the lower number that ends with zero
Example: 52437 is rounded to the nearest hundred thousand is 52000
Sorry if you don't understand I'm just bad at explaining :) T^T
Write the following as anas an inequality:The sum of x and y is no greater than 2.
The inequality no greater than mean at most or maximum.
The inequality can be written as,
[tex]x+y\leq2[/tex]Thus, the above inequation represents the given inequality.
Given f(x) = 4x -5; what is f(4)?
The domain for the relation below is {x| -6
We need to find the point given the domain and range of the relation:
For domain and range, the result includes the number. Hence, the end values are given by the points.
For point C:
(-6,4)
Because point c is on quadrant two, where x is negative and y is positive.
Also, it takes the higher y value.
For point D:
(6,3)
Because point D is on quadrant 1, where x is positive and y is also positive.
