Hello there. To solve this question, we'll find how many times George's grandpa is older than his grandson.
First, this is also called the ratio of the ages between George and his grandpa.
To find this, we divide their ages in the order Grandpa : Grandson as following:
[tex]\frac{George^{\prime}s\text{ Grandpa age}}{\text{George's age}}=\text{ }\frac{72}{8}[/tex]Simplify the fraction by a factor of 8
[tex]9[/tex]This is how many times George's grandpa is older than him.
The number of infected
zombies triples every
hour. How many
zombies are there after 6
hours if one zombie was
initially infected?
Answer:
f(x) = 4(1.15)6.
Step-by-step explanation:
84 points + brainliest if well explained and correct:
During a thunderstorm at a sports event, a detector goes off to let participants know there is lightning in the area so people can seek shelter. The accuracy of the lightning detector is summarized in the table.
Lightning detector activates Lightning detector does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
What is the ratio of false positives to false negatives in this scenario? Round your answer to one decimal place.
0.1
1.5
2.3
3.5
The ratio of false positives to false negatives is (d) 3.5
How to determine the ratio?The table of values is given as
Activates. Does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
The false negative is when there is lighting and it does not activate
So, we have
False negative = 2%
The false positive is when there is no lighting and it activates
So, we have
False positive = 7%
When represented as ratio, we have
Ratio = 7% : 2%
So, we have
Ratio = 7 : 2
This gives
Ratio = 7/2
Evaluate
Ratio = 3.5
Hence, the ratio is (d) 3.5
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octavia simplified the expression as shown explain octavia’s error and correct her work
To simplify
[tex](3x^9)^2(3x^2)^4[/tex]First of all, Octavia error can be spotted from the correct steps below
Step1: Expand the expression
[tex]3^2\times x^{9\times2}\times3^4\times x^{2\times4}=3^2\times x^{18}\times3^4\times x^8[/tex]Step2: Collect like terms
[tex]3^2\times3^4\times x^{18}\times x^8[/tex]Step 3: Simplify by using exponents laws
[tex]3^{2+4}\times x^{18+8}=3^6\times x^{26}[/tex]Step 4: Combine the terms.
The value is
[tex]729x^{26}[/tex]Her error was that she didn't apply the exponents' law properly.
One of the laws she violated was
[tex](a^b)^c=a^{b\times c}[/tex]Her mistake was that she did
[tex](a^b)^c=a^{b+c}\text{ which is wrong}[/tex]So she missed it from our step 1 above
Leah is buying titles for her bathroom. Each tile is 3/8 foot wide and covers an area that is 7/3 square feet. The bathroom floor is in the shape of a rectangle. She is putting 8 tiles along the longer wall of the bathroom and 5 tiles along the shorter wall of the bathroom. What is the perimeter of the bathroom? The bathroom and one tile are pictured below.
The perimeter of the rectangular floor is 103 feet.
What are rectangles?With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel.Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's length is its longer side, while its width is its shorter side.So, the perimeter of the bathroom floor will be:
First, let the length of the tiles be 'x'.Now,
7/3 = x × 3/8x = 7/3 ÷ 3/8x = 7/3 × 8/3x = 56/9So, the length of the tile is 56/9.
Now, the l and b of the rectangular floor will be:
56/9 × 8 + 3/8 × 5448/9 + 15/88(448) + 9(15)/723584 + 135/723719/7251.65Formula is: 2(l+b)
Now,
2 × 51.65103.3Rounding off: 103 feet
Therefore, the perimeter of the rectangular floor is 103 feet.
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The aspect ratio for a computer screenis 118. If the width of the computer screen is 13.5inches. What is the begi of the mean?Answer question 1 photo attached
The aspect ratio for a computer screen is
if the width equals 13.5, then the height is:
[tex]h=\frac{13.5}{1.8}=7.5[/tex] 3.152 written as an improper fraction or a mixed number and explained how it was done.
Answer: 3.152 as an improper fraction would be: 394 / 125
Step-by-step explanation: You can take any number, such as 3.152, and write a 1 as the denominator to make it a fraction and keep the same value, like this:
3.152 / 1
To get rid of the decimal point in the numerator, we count the numbers after the decimal in 3.152, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction:
3152 / 1000
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of 3152 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following:
394 / 125
(have a nice day)
12)50 students took a quiz with five questions. The frequency table below shows the results of the quiz. Use the frequency table to answer the following questions. ValueFrequencyRelative FrequencyCumulative Frequency040.084180.1612260.1218320.04204150.3355150.350a)How many students answered exactly 3 questions correctly?Number of students answered exactly three questions = 2b)How many students answered less than 3 questions correctly?c)What proportion (percent) of students answered exactly 4 questions correctly?
From the table, we have:
• The first column (Value),: indicates the # of correct answers,
,• The second column (Frequency),: indicates the # of students that answer the # of correct answers to the left in the table,
,• The third column (Relative Frequency),: indicates the proportion of the # of students to the total,
,• The fourth column (Cumulative Frequency),: gives the sum of the previous frequencies up to that row.
Using these data, we answer the questions:
a) Looking at the column Frequency for Value = 3, we find that 2 students answered exactly 3 answers correct.
b) Looking at the column Cumulative Frequency for Value = 2 (the previous value to 3), we find that 18 students answered less than 3 questions correctly.
c) Looking at the column Relative Frequency for Value = 4, we find that 0.3 = 0.3 * 100% = 30% of the students answered exactly 4 questions correctly.
Answera) 2
b) 18
c) 30%
what is the answer to 8.34x0.5
Write an equation in slope-intercept form for the graph shown.
Answer:
y= 2x-3
Step-by-step explanation:
4/2 OR 2 is the slope
-3 is the intercept
Write the equation of the line in fully simplified slope-intercept form.
pls helpp me
Answer:
y= 1/5x -7
Step-by-step explanation:
1/5 is the slope
-7 is the y-intercept
If a = [tex]\frac{2 + \sqrt{5}}{2}[/tex], find the value of [tex]a^{2} + \frac{1}{a^{2} }[/tex].
The value of [tex]a^{2} +\frac{1}{a^{2} }[/tex] if [tex]a=\frac{2+\sqrt{5} }{2}[/tex] is solved to be
5.1How to determine the equationThe equation is solved by substituting for a in the given equation [tex]a^{2} +\frac{1}{a^{2} }[/tex]
[tex]a^{2} +\frac{1}{a^{2} }[/tex]
substituting for a
[tex](\frac{2+\sqrt{5} }{2})=(1+\frac{\sqrt{5} }{2})[/tex]
[tex](1+\frac{\sqrt{5} }{2})^{2} =(1+\frac{\sqrt{5} }{2})*(1+\frac{\sqrt{5} }{2})=1+2\frac{\sqrt{5} }{2} +\frac{5}{4}=\sqrt{5} +\frac{9}{4}=4.48607[/tex]
= 4.8607 + 1/4.48607
= 5.0664
Substituting the value of a in the equation and solving resulted to 5.1
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Which situation could be represented by the graph
Answer:
what graph
Step-by-step explanation:
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?A 4B. -2C -1D. 1
You need to know the following:
1. The "difference" is the result of a subtraction.
2. The word "times" indicates a multiplication.
3. The sum is the result of an addition.
Let be "n" the number mentioned in the exercise.
Knowing the explained above, you know that "the difference of a number and 6" can expressed as:
[tex]n-6[/tex]And "5 times the sum of the number and 2" can be expressed as:
[tex]5(n+2)[/tex]Therefore, "the difference of a number and 6 is the same as 5 times the sum of the number and 2" can be written as the following equation:
[tex]n-6=5(n+2)[/tex]Now, in order to find the number, you must solve for "n":
[tex]undefined[/tex]It is one question the three images are the options for answers to the question.
Whats the Square root of 32 to the power of 5
Answer:
2^25/2
Step-by-step explanation:
We express them as a power of 2 using laws of indices
What is the solution to the missing side of the figure, rounded to the nearest tenths place?A) 16.2.B.) √261C) 16.1D.) 261
The figure appears to be a triangle with the following measures:
Opposite Side = a = 6
Adjacent Side = b = 15
Hypotenuse = c = unknown
To be able to find the measure of the unknown side, since it appears to be a right triangle, we will be using the Pythagorean Formula:
[tex]\text{ c}^2=a^2+b^2[/tex][tex]\text{ c = }\sqrt[]{a^2+b^2}[/tex][tex]\begin{gathered} \text{ c = }\sqrt[]{(6)^2_{}+(15)^2} \\ \end{gathered}[/tex][tex]\text{ = }\sqrt[]{36\text{ + 225}}[/tex][tex]\text{ = }\sqrt[]{261}[/tex][tex]\text{ c = }\sqrt[]{261}\text{ = 16.1554944214}[/tex]What is the value of x?
Answer:
75 degree
Step-by-step explanation:
We know that a straight angle is 180 degree
and in the picture we can see an angle of 105 degree
so we get 180-105= 75 degree
Got It? Do these problems to find out.
b. y = x-5
c. y = -2x
pls help, thanks!
Answer:
For b, you just start at (0,-5)(go down 5 on the y-axis), and go one up, one over to the right, and for c, just start at (0,0) and go right one, up 2
Step-by-step explanation:
Can someone please explain to me why -4² = -16?
Answer:
-4 x -4 = -16
4 x 4 = 16
^2 or to the power of 2 basely means 4 times itself, because 2.
There are 83 skiers in line to ride the chair lift. If each chair seats 6 people, how many skiers will be on the last chair?
Answer:
4 people will be on the last chair.
Step-by-step explanation:
60 divided by 5 is 12. There will be 12 full seats. 64 - 60 is 4 so there will be 4 more on the last chair.
Hope this helped!
-. Write an equation in slope-intercept form that
describes the line through the points (2,7) and
(-1,-5).
The slope-intercept form equation of the line is y=(-2/3)x-(17/3) when the line is passing through the points (2,7) and (-1,-5).
What is meant by slope?Finding the ratio of vertical change to horizontal change between any two distinct points on a line yields the slope. Occasionally, the ratio is written as a quotient, which produces the same number for every two distinct points on the same line. A negative rise refers to a diminishing line. The line could be functional, set by a road surveyor, or depicted in a diagram that represents a road or a roof as a description or a plan.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope.
The slope-intercept form is y=mx+c
Given points are (2,7) and (-1,-5)
Slope m= (y₂-y₁)/(x₂-x₁)
m=(-5+7)/(-1-2)
m=-2/3
By substituting m value in the above equation we get,
y=(-2/3)x + c
Given that, the above equation is passing through the point (-1,-5)
-5=(-2/3)(-1)+c
c=-5-(2/3)
c=-17/3
y=(-2/3)x-(17/3)
Therefore, the equation of the slope-intercept form is y=(-2/3)x-(17/3)
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Find z_1 x z_2 for z_1 = 9(cos225° + isin225°) and z_2 = 3(cos45° + isin45°).The 'z' is all subscript.
Using Euler's Formula:
[tex]re^{i\theta}=r(\cos (\theta)+i\sin (\theta))[/tex]Since:
[tex]\begin{gathered} z1=9(\cos (225)+i\sin (225)) \\ z2=3(\cos (45)+i\sin (45)) \\ \end{gathered}[/tex]We can rewrite them as:
[tex]\begin{gathered} z1=9e^{225i} \\ z2=3e^{45i} \end{gathered}[/tex]So:
[tex]\begin{gathered} z1\times z2=(9e^{225i})(3e^{45i})=27e^{225i+45i}=27e^{270i} \\ so\colon \\ z1\times z2=27(\cos (270)+i\sin (270)) \end{gathered}[/tex][tex]\begin{gathered} a=r\cos (\theta) \\ b=r\sin (\theta) \\ where \\ r=27 \\ \theta=270 \end{gathered}[/tex]So:
[tex]undefined[/tex]A pack of cinnamon-scented pencils sells for $8.00. What is the sales tax rate if the total cost of the pencils Is $8.56 The sales tax rate is ___%
To find the tax rate we can use the rule of three.
[tex]\begin{gathered} 8\rightarrow100 \\ 8.56\rightarrow x \end{gathered}[/tex]Then,
[tex]x=\frac{8.56\cdot100}{8}=107[/tex]Now, since 8.56 dollars represents 107% of the prices, this means that the tax rate is 7.
14. You buy a package that contains 10 1/2 cups of fruit and nut mix. How many snack bags each with 3/4 cup of fruit and nut mix can you fill from the package?
Given:
The package contains 10 1/2 cups of fruit and nut mix
When need to snack bags, each bag contain 3/4 cup
So, to find the number of bags, divide 10 1/2 by 3/4
so, the number of bags =
[tex]10\frac{1}{2}\div\frac{3}{4}=\frac{21}{2}\div\frac{3}{4}=\frac{21}{2}\cdot\frac{4}{3}=7\cdot2=14[/tex]So, the answer is: the number of bags = 14
b. A family of four went to see a live concert in Vancouver. Each family member bought
a commemorative concert T-shirt, which cost 1/5 of the price of a ticket. The total bill
for 4 tickets and 4 T-shirts was $384. How much did each ticket and each T-shirt cost?
The cost of 1 ticket is $80 and the cost of 1 T-Shirt is $16 .
In the question ,
it is given that ,
a family of four people went to see a live concert in Vancouver ,
and the price of T-shirt is 1/5 of the price of the ticket .
let the price of 1 ticket be = x ,
so , the price of 1 T-Shirt be = x/5 .
also given that the bill for 4 tickets and 4 T-Shirts was $384 ,
that means
4x + 4x/5 = 384
taking LCM as 20 and solving further ,
we get,
20x/5 + 4x/5 = 384
24x/5 = 384
24x = 384*5
24x = 1920
x = 1920/24
x = 80
the cost for T-Shirt = 80/5 = 16
Therefore , The cost of 1 ticket is $80 and the cost of 1 T-Shirt is $16 .
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I NEED HELP! ASAP! WILL GIVE 50 POINTS!
Answer:
Of 20,000 people that apply, 6300 actually enroll.
Step-by-step explanation:
70% of 20,000 is 14,000
45% of 14,000 is 6,300
The measures of two complementary angles are described by the expressions (11x−11)° and (16x−7)°. Find the measures of the angles.I know complementary when their measures add to 90 degrees. but I'm not to sure where to plug the numbers in
Given:
[tex](11x-11)^{\circ}and(16x-7)^{\circ}\text{ forms an complementary angles.}[/tex][tex]\begin{gathered} 11x-11+16x-7=90 \\ 27x-18=90 \\ 27x=90+18 \\ 27x=108 \\ x=\frac{108}{27} \\ x=4 \end{gathered}[/tex]Which of the following terms is defined as a set of all points in a planethat are a given distance from a point?O CircleO Line segmentO RayO Parallel line
Given:
A set of all points in a plane that are a given distance from a point.
Required:
To choose the correct option for the given definition.
Explanation:
A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.
Final Answer:
A set of all points in a plane that are a given distance from a point is called circle.
-2/3 (x-7) = 1/6 (x+1) -3
Answer: x = 9
Step-by-step explanation:
We will isolate the variable x to solve this equation.
Given:
-2/3 (x-7) = 1/6 (x+1) -3
Distribute:
-2/3x + 14/3 = 1/6 (x+1) -3
-2/3x + 14/3 = 1/6x + 1/6 -3
Combine like terms on the right side using subtraction:
-2/3x + 14/3 = 1/6x - 17/6
Subtract 1/6x from both sides of the equation:
-5/6x + 14/3 = - 17/6
Subtract 14/3 from both sides of the equation:
-5/6x = -15/2
Divide both sides of the equation by -5/6:
x = 9
can someone help me with this assignment pls
The order pair (3, 14) is from the given scatter plot.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
• A scatter plot with increasing values of both variables can be said to have a positive correlation.
• A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.
In the given scatter plot, the order pair with x-coordinate 3 is 14
So, the order pair is (3, 14)
Therefore, the order pair (3, 14) is from the given scatter plot.
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