Final answer:
Marcus is incorrect, not because the result may not be rational, but because of his reasoning. An integer raised to a negative integer exponent leads to the base being inverted and raised to the positive exponent, but the result is still a rational number.
Explanation:
Marcus is incorrect in stating that any time an integer is raised to an integer exponent, the result is a rational number. To understand why, we should look at the case when an integer is raised to a negative integer exponent. For example, 3-2 is equal to 1 / (32) which simplifies to 1 / 9. A negative exponent inverts the base number and raises it to the positive of that exponent, which means the result is still a rational number, as it's a quotient of two integers. Therefore, the correct statement is that the result of an integer raised to any integer exponent is indeed a rational number, as the quotient of two integers (for negative exponents) is also a rational number.
A circle is divided into 8 sectors. Each sector has an area of approximately 5 square inches. What is the approximate area of the circle?
Question 5 options:
A. 25 square inches
B. 40 square inches
C. 15.7 square inches
D. 78.5 square inches
A baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold. How many muffins were sold by noon?
Answer:
27 muffins.
Step-by-step explanation:
We have been given that a baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold.
To find the number of muffins sold by noon let us find 45% of 60.
[tex]\text{The number of muffins sold by noon}=\frac{45}{100}\times 60[/tex]
[tex]\text{The number of muffins sold by noon}=0.45\times 60[/tex]
[tex]\text{The number of muffins sold by noon}=27[/tex]
Therefore, 27 muffins were sold by noon.
Solve for the missing variables. (Geometry)
Answer:
92 degrees is x
88 degrees is y
Answer:
x=92. y= 88
Step-by-step explanation:
all three corners of a tri. equal 180
so 39+49=88
180-88=92 now y and x= 180 also so y
Tours of the art museum are offered every 1/3 hour starting at 10A.M. The museum closes at 4:00 P.M. How many tours are offered eavch day?
Answer:
Each day, [tex]18[/tex] tours are offered.
Step-by-step explanation:
We were given that, the museum starts at,
10:00 AM and closes at 4:00 PM.
The total duration is [tex]4:00PM-10:00AM=16:00GMT-10:00GMT=6hours[/tex]
Since the tour of the museum are offered every [tex]\frac{1}{3}[/tex] hour each day, we can calculate the number of tours that will be offered within the 6 hours as follows
[tex]Number\:of\:tours=\frac{6}{\frac{1}{3} }[/tex]
We rewrite to obtain,
[tex]Number\:of\:tours=6\div \frac{1}{3}[/tex]
We multiply by the reciprocal of the second fraction to get,
[tex]Number\:of\:tours=6\div \frac{3}{1}=18[/tex]
Therefore 18 tours will be offered each day in the art museum.
Answer: Therefore, the art museum offers 18 tours each day.
Step-by-step explanation: The art museum offers tours every 1/3 hour starting at 10 A.M. and closes at 4:00 P.M. To determine how many tours are offered each day, we need to find the total number of 1/3 hour intervals between 10 A.M. and 4:00 P.M.
First, we need to convert the closing time to the same format as the starting time. Since there are 60 minutes in an hour, we can write 4:00 P.M. as 16:00.
Next, we calculate the number of hours between the starting and closing times by subtracting 10 from 16, which gives us 6 hours.
Since there are 3 intervals in each hour, we multiply the number of hours by 3 to find the total number of 1/3-hour intervals. In this case, 6 hours multiplied by 3 equals 18 intervals.
Therefore, the art museum offers 18 tours each day.
Place the decimal point in the answer below to make it correct. Explain your reasoning
Answer:
AC is greater than BC because segment AC is the hypotenuse of right triangle ABC, and the hypotenuse is the longest side of a right triangle.
Will mark brainliest!! Help plzz
Answer:
-4 is the simplified form. of the given expression.
Step-by-step explanation:
We have been given an expression:
[tex]-64^\frac{1}{3}[/tex]
We can rewrite 64 as [tex]4^3[/tex]
the given expression will be rewritten as:
[tex](-(4)^3)^\frac{1}{3}[/tex]
powers will get cancel out we get:
[tex]-4[/tex] is the required simplified form.
A cruise ship can cover 17 nautical miles in 306 minutes. How many nautical miles will it travel in 162 minute
Set up a proportion:
17 miles in 306 minutes, write as 17/306
X miles in 162 minutes, write as X/162
Now set to equal and solve:
17/306 = x/162
Cross multiply:
17 * 162 = 306 *x
2754 = 306x
Divide both sides by 306:
x = 2754 / 306
x = 9
It will travel 9 nautical miles.
Which of these sets of points lie within plane w?
Justin and Jason are building a fort. They need 250 pieces of wood. Justin can hammer 10 1/4 pieces of wood an hour. Jason can hammer 9 1/2 in one hour. How many hours will it take them to finish the fort?
Answer: 12 hours
Step-by-step explanation:
1.) add 10 1/4 and 9 1/3. You’ll get 19.75
2.) divide 250 by 19.75. You’ll get something close to 12.6582278481 if you use appendix zeros.
3.) round 12.6582278481 to the nearest whole number. It will be 12. Hope this helps :)
Write an equation of the line,in point slope form, that passes through the two given points. Points: (-13,9),(11,-3)
It’s for number 7. I know it shows me the right answer but I am doing corrections and I need some help in how to solve it. Please help!
The equation in point slope form is y-y1 = m(x-x1)
The first point given is (-13,9) so this is used for Y1 and X1.
m is the slope which is found by the change in Y over the change in x.
The slope is -3 - 9 / 11 - -13, which equals -1/2
So the equation becomes y-9 = -1/2(x+13)
Answer:
y-9=-1/2(x+13)
Step-by-step explanation:
To find the slope for the line, we use
m = (y2-y1)/(x2-x1)
since we know the points( -13,9) and (11,-3)
m= (-3-9)/(11--13)
=(-3-9)/(11+13)
=-12/24
= -1/2
We can use the point slope form to make the equation for the line
y-y1=m(x-x1)
y-9=-1/2(x--13)
y-9=-1/2(x+13)
A jewelry store purchases a necklace for 150. They markup the necklace 75% how much will the jewelry store sell the necklace for ?
The selling price of the necklace is calculated by adding a 75% markup to the original purchase price of $150, which results in a selling price of $262.50.
To calculate the selling price of a necklace that a jewelry store purchased for $150 with a 75% markup, you first need to find out how much 75% of the purchase price is and then add that to the original purchase price. To do this, multiply the purchase price, $150, by 75% (or 0.75). This calculation gives you the markup amount:
Markup amount = $150 imes 0.75 = $112.50
After finding the markup amount, you add it to the original purchase price to find the selling price:
Selling price = Original purchase price + Markup amount
Selling price = $150 + $112.50 = $262.50
Therefore, the jewelry store will sell the necklace for $262.50.
Robert climbed 775775 steps in 12\dfrac1212 2 1 ? minutes. How many steps did he average per minute?
Answer:
62 steps per minute.
Step-by-step explanation:
We have been given that Robert climbed 775 steps in [tex]12\frac{1}{2}[/tex] minutes.
To find the the average steps per minute we will divide 775 by [tex]12\frac{1}{2}[/tex].
[tex]\text{The average steps per minute}=775\div 12\frac{1}{2}[/tex]
Let us convert our mixed fraction into improper fraction.
[tex]\text{The average steps per minute}=775\div \frac{25}{2}[/tex]
Dividing a number by a fraction is same as multiplying the number by the reciprocal of fraction.
[tex]\text{The average steps per minute}=775\times \frac{2}{25}[/tex]
[tex]\text{The average steps per minute}=31\times2[/tex]
[tex]\text{The average steps per minute}=62[/tex]
Therefore, Robert climbed 62 steps per minute.
Answer:
62 Steps per minute. <3
Step-by-step explanation:
Consider the triangles shown. If mUTV < mUTS < mSTR, which statement is true?
Answer:
The true statement is UV < US < SR ⇒ 1st statement
Step-by-step explanation:
"I have added screenshot of the complete question as well as the
diagram"
* Lets revise the hinge theorem
- If two sides of one triangle are congruent to two sides of another
triangle, and the measure of the included angle between these two
sides of the first triangle is greater than the measure of the included
angle of the second triangle then the length of the third side of the
first triangle is longer than the length of the third side of the second
triangle
* Lets solve the problem
- The figure has three triangles have a common vertex T
- m∠UTV < m∠UTS < m∠STR
- From the hinge theorem above
∵ The side opposite to ∠UTV is VU
∵ The side opposite to ∠UTS is US
∵ The side opposite to ∠STR is SR
∵ m∠UTV < m∠UTS < m∠STR
∴ UV < US < SR
* The true statement is UV < US < SR
Answer:
VU<US<SR by the hinge theorem
Step-by-step explanation:
a storage container is a rectangular prism with a volume of 392 cubic inches. the height of the container is 3 inches less than its length and its width is twice the length. what are the dimensions of the container?
Answer:
Step-by-step explanation:
Let the length of the rectangular prism = x inches
Width of the rectangular prism = 2 x length = 2x inches
Height of the rectangular prism = 3 inches less than the length = (x -3) inches
Volume of the rectangular prism = length x width x height = 392 cubic inches
= (2x) inches x (x) inches x (x -3) inches = 392 cubic inches
= x2(x-3) = 196 cubic inch
X = 8.59 inch
Length of the rectangular prism = x inches = 7 inch
Width of the rectangular prism = 2 x length = 2 x 7 inch = 14 inch
Height of the rectangular prism = 3 inches less than the length = (x -3) inches = 7 – 3 = 4 inch
The dimensions of the storage container are 7 inches in length, 14 inches in width, and 4 inches in height. The volume equation is solved for length by substituting the relationships between height, width, and length into the formula for volume.
To find the dimensions of a rectangular prism storage container with a volume of 392 cubic inches, we need to set up equations based on the information given. The height (h) of the container is 3 inches less than its length (l), so h = l - 3. The width (w) of the container is twice the length of the container, so w = 2l. Knowing that volume = length * width * height (V = lwh), we can substitute the expressions for h and w into the volume equation to obtain an equation with one unknown:
V = l * (2l) * (l - 3)
Substituting the known volume into the equation, we get:
392 = l * (2l) * (l - 3)
This is a cubic equation that can be solved for l (the length of the container). Once l is found, we can also find h and w since they are defined in terms of l.
Let's solve the equation:
[tex]392 = 2l^2 * (l - 3)[/tex]
Divide both sides by 2 to simplify:
[tex]196 = l^2 * (l - 3)[/tex]
Now we expand and solve for l:
[tex]196 = l^3 - 3l^2[/tex]
Moving all terms to one side gives:
[tex]l^3 - 3l^2 - 196 = 0[/tex]
By trial and error or using a cubic equation solver, we find that l = 7 inches. Now we can find the height and width:
h = l - 3 = 7 - 3 = 4 inches
w = 2l = 2 x 7 = 14 inches
Therefore, the dimensions of the storage container are 7 inches in length, 14 inches in width, and 4 inches in height.
Judy worked 8 hours and Ben worked 10 hours. Their combined pay was $80. When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65. Find the hourly rate of pay for each person
Answer:
Judy = $5/hr
Ben = $4/hr
Step-by-step explanation:
Judy's hours at work - x
Ben's hours at work - y
8x + 10y = 80
9x + 5y = 65
Given these two equations above, we get:
10y = 80 - 8x, which means y = 8 - 0.8x.
Substitute y in the second equation with 8 - 0.8x, so we have:
9x + 5 (8 - 0.8x) = 65
9x + 40 - 4x = 65
5x = 25
x = 5
Come back to the first equation, substitute x:
8*5 + 10y = 80
10y = 80 - 40
y = 4
An electrician sent Bonnie an invoice in the amount of 'a' dollars for 6 hours of work that was done on Saturday. The electrician charges a weekend fee 'f' in addition to an hourly rate 'r'. Bonnie knows what the weekend fee is. Write a formula Bonnie can use to find 'r', the rate the electrician charges per hour.
Answer:
(a-f)/6 = r
Step-by-step explanation:
The total Bonnie must pay is the weekend fee plus the hourly rate times the hours worked
Cost = weekend fee * hourly rate* hours
hours = 6
weekend fee =f
hourly rate = r
Cost = a dollars
Substituting in what we know
a = f+ 6r
We want to solve for r
Subtract f from each side
a-f =f-f +6r
a-f = 6r
Divide each side by 6
(a-f)/6 = 6r/6
(a-f)/6 = r
Which ordered pair is a solution to the inequality? 4x + y > - 6
A) (1, -12)
B) (0, -9)
C) (-1, -1)
D) (-3, 0)
The answer: C) (-1, -1)
The table below illustrates the decay of a sample of radioactive uranium. Time in Days, x 0 1 2 3 4 5 Sample Remaining (grams), U 500 255 130 66 34 17 Which equation best models this set of data where U represents the amount of sample remaining, in grams, at time x?
[tex]\underline{\ x|\ \ 0\ \ |\ \ 1\ \ |\ \ 2\ \ |\ \ 3\ \ |\ \ 4\ \ |\ \ 5\ \ |}\\U|500\ |\ 255|\ 130|\ 66\ \ |\ 34\ |\ \ 17\ |\\\\U=a(b)^x\\\\for\ x=0,\ U=500\\\\500=a(b)^0\\\\500=a(1)\to \boxed{a=500}\\\\for\ x=1,\ U=255\\\\255=500(b)^1\\\\255=500b\qquad\text{divide both sides by 500}\\\\b=\dfrac{255}{500}\\\\b=\dfrac{255:5}{500:5}\\\\b=\dfrac{51}{100}\to \boxed{b=0.51}\\\\\text{Therefore we have the equation of the function:}\\\\U=500(0.51)^x[/tex]
[tex]\text{Check for other values of x:}\\\\for\ x=2\\\\U=500(0.51)^2=130.05\approx130\qquad CORRECT\\\\for\ x=3\\\\U=500(0.51)^3=66.3255\approx66\qquad CORRECT\\\\for\ x=4\\\\U=500(0.51)^4=33.826\approx34\qquad CORRECT\\\\for\ x=5\\\\U=500(0.51)^5=17.25125\approx17\qquad CORRECT[/tex]
[tex]Answer:\ \boxed{U=500(0.51)^x}[/tex]
Somebody please help with this problem
Step-by-step explanation:
We have been given that AE=BE and [tex]\angle1\cong \angle2[/tex].
We can see that angle CEA is vertical angle of angle DEB, therefore, [tex]m\angle CEA=m\angle DEB[/tex] as vertical angles are congruent.
We can see in triangles CEA and DEF that two angles and included sides are congruent.
[tex]\angle 1\cong \angle 2[/tex]
[tex]AE=BE[/tex]
[tex]\angle CEA\cong\angle DEB[/tex] or [tex]\angle 3\cong \angle 4[/tex]
Therefore, [tex]\Delta CEA\cong \Delta DEB[/tex] by ASA postulate.
Since corresponding parts of congruent triangles are congruent, therefore CE must be congruent to DE.
Write the equation of the conic section with the given properties:
An ellipse with vertices (-8, 0) and (8, 0) and a minor axis of length 10.
Answer:
[tex]\frac{x^2}{64} + \frac{y^2}{25} =1[/tex]
Step-by-step explanation:
An ellipse with vertices (-8, 0) and (8, 0)
Distance between two vertices = 2a
Distance between (-8,0) and (8,0) = 16
2a= 16
so a= 8
Vertex is (h+a,k)
we know a=8, so vertex is (h+8,k)
Now compare (h+8,k) with vertex (8,0) and find out h and k
h+8 =8, h=0
k =0
a minor axis of length 10.
Length of minor axis = 2b
2b = 10
so b = 5
General formula for the equation of horizontal ellipse is
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b} =1[/tex]
a= 8 , b=5 , h=0,k=0. equation becomes
[tex]\frac{(x-0)^2}{8^2} + \frac{(y-0)^2}{5} =1[/tex]
[tex]\frac{x^2}{64} + \frac{y^2}{25} =1[/tex]
aiutami con la mia matematica
Una lampada è in vendita e il suo prezzo è ridotto da $ 80 a $ 50.
Qual è la percentuale di diminuzione?
0.3
0.375
0.625
30
37.5
62.5
Kevin compra 4 sedie pieghevoli. Ogni sedia costa $ 13,50. L'imposta sulle vendite è del 6,5%.
Qual è l'importo delle tasse di vendita per gli acquisti di Kevin?
Inserisci la tua risposta nella casella.
Quinn has a large family. She has 4 cousins who live in Texas, 3 cousins who live in Nebraska, and 9 cousins who live in Michigan. What is the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan?
Answer:
the required ratio is: 4:9
Step-by-step explanation:
Quinn has 4 cousins who live in Texas, 3 cousins who live in Nebraska, and 9 cousins who live in Michigan.
We have to find the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan
The required ratio is:
[tex]Ratio=\frac{\text{Number of Quinn's cousins who live in Texas}}{\text{cousins who live in Michigan}}[/tex]
[tex]Ratio=\frac{4}{9}[/tex]
Hence, the required ratio is: 4:9
The ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan is 4:9. This means for every 4 cousins in Texas, there are 9 cousins in Michigan.
Explanation:The subject of this question is Mathematics. Specifically, it involves calculating ratios. In this case, the student wants to know the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan.
The ratio of something is simply a way to compare quantities. Here, we have 4 cousins in Texas and 9 cousins in Michigan. So, to get the ratio from Texas to Michigan, we simply write it as '4:9' or we can say, 'for every 4 cousins in Texas, there are 9 cousins in Michigan'.
In summary, the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan is 4:9.
Learn more about Ratio here:https://brainly.com/question/32531170
#SPJ3
Was he correct? Why or why not?
D
Step-by-step explanation:Angle 7π/6 is π/6 below the negative x-axis in the 3rd quadrant. Its cosine will be -(√3)/2.
Angle 11π/6 is π/6 below the positive x-axis in the 4th quadrant. Its cosine will be (√3)/2.
The cosines have the same magnitude, but their signs are opposite each other. Jeremy was not correct.
Help me with this! Brainliest for the best answer.
Answer: -3/5
Step-by-step explanation:
All you have to do is use rise over run!
basically form a triangle and count how much up and how much over. :D
Fred is running on the school track. He can run 10 3 4 laps in 4 5 of an hour. How many laps can Fred run in one hour?
Answer:
[tex]13\frac{7}{16}[/tex] laps can Fred run in one hour.
Step-by-step explanation:
Given Statement: Fred is running on the school track. He can run [tex]10\frac{3}{4}[/tex] laps in [tex]\frac{4}{5}[/tex] of an hour.
Unit rate are expressed as a quantity of 1, such as 3 feet per second or 7 miles per hour, they are called unit rates
From the given condition we have;
In [tex]\frac{4}{5}[/tex] he can run [tex]\frac{43}{4}[/tex] laps
Unit rate per hour = [tex]\frac{\frac{43}{4} }{\frac{4}{5} }[/tex]
=[tex]\frac{43}{4} \times \frac{5}{4} = \frac{215}{16}[/tex] laps
Therefore, Fred can run in one hour is, [tex]13\frac{7}{16}[/tex] laps.
Final answer:
To determine how many laps Fred can run in one hour, we used a proportion equation, converting 10 3/4 laps to an improper fraction and then solving for x. Fred can run approximately 13.44 laps in one hour.
Explanation:
Calculating Laps per Hour
To find out how many laps Fred can run in one hour, we need to perform a simple proportion based on the information given. Fred can run 10 3/4 laps in 4/5 of an hour. To find out how many laps he can run in a full hour (1 hour), we set up the proportion equation:
\[\left(\frac{10 \frac{3}{4}}{\frac{4}{5}}\right) = \left(\frac{x}{1}\right)\]
First, we convert 10 3/4 to an improper fraction, which is \(\frac{43}{4}\). Then we solve for \(x\) by multiplying both sides by 1, which simplifies our proportion to:
\[x = \frac{43}{4} \times \frac{5}{4}\]
Next, we multiply the numerators and then the denominators:
\[x = \frac{43 \times 5}{4 \times 4}\]
\[x = \frac{215}{16}\]
Finally, we divide 215 by 16 to get \(x = 13.4375\), which means Fred can run approximately 13.44 laps in one hour.
Sis buys 5 pieces of fabric each piece of fabric is 1 7/10 yards long what is the total length of the fabric she buys one yard of the fabric cost $5 how much does she pay for all five pieces of fabric
In basketball game, elena scores twice as many points as tyler.Tyler scores four points fewer than noah,and noah scores three times as many points as mai if mai scores 5 points how many points did elena score explainyour reasoning
Answer:
Step-by-step explanation:
Start at the end and work backwards to do this one. Mai scored 5 points.
If Noah scores three times what Mai scores, then:
Noah = 3(5) = 15
If Tyler scores 4 points less than Noah, then:
Tyler = 15 - 4 = 11
If Elena scores twice what Tyler scores, then:
Elena = 2(11) = 22
MATH HELP PLEASE!!
find the area of the shaded region.
use the formula A= pi r^2 to find the area of the circle.
a. 8pi x + 24pi
b. 8pi x - 24pi
c. x^2 + 8pi x + 24pi
d. x^2 +8pi x - 24pi
Answer:
d
Step-by-step explanation:
Lucy planted a lemon tree and a cherry tree. The lemon tree is 6 feet tall. The cherry tree is 3 7/10 times as tall as the lemon tree. How tall is Lucy's cherry tree?
To calculate the height of Lucy's cherry tree, we first convert 3 7/10 to an improper fraction, resulting in 37/10. Then we multiply the height of the lemon tree (6 feet) by 37/10 to get 22.2 feet. Thus, the cherry tree is 22.2 feet tall.
To find the height of Lucy's cherry tree, which is 3 7/10 times as tall as her lemon tree, we start with the known height of the lemon tree, which is 6 feet tall. We then multiply this height by the factor 3 7/10 to determine the height of the cherry tree.
First, let's convert the mixed number to an improper fraction to simplify the calculation:
Multiply the whole number part (3) by the denominator of the fraction part (10): 3 × 10 = 30.Add this to the numerator of the fraction part (7): 30 + 7 = 37.Now we have an improper fraction of 37/10.Next, we'll multiply the height of the lemon tree by this fraction:
6 feet × 37/10 = (6 × 37) / 10 = 222 / 10 = 22.2 feet.
So, the height of Lucy's cherry tree is 22.2 feet tall.
In my fish tank, the ratio of red fish to blue fish is 1:5. There are 15 blue fish. How many red fish are there?
To find the number of red fish in a tank where the ratio of red to blue fish is 1:5 and there are 15 blue fish, divide the number of blue fish by the blue part of the ratio (15 ÷ 5) and multiply by the red part (1), resulting in 3 red fish.
Explanation:The question asks how many red fish are there in a fish tank if the ratio of red fish to blue fish is 1:5 and there are 15 blue fish. To solve this, you can use the ratio provided. Since the ratio of red to blue fish is 1:5, for every 1 red fish, there are 5 blue fish.
Given there are 15 blue fish, you can divide the number of blue fish by the ratio part for blue fish to find out how many parts of red fish there are.
Step 1: Find the ratio part representing red fish. It is 1.
Step 2: Divide the number of blue fish by the blue ratio part (5) to find how many times the ratio fits into the blue fish population. 15 blue fish ÷ 5 = 3.
Step 3: Multiply the result by the red ratio part. 3 × 1 = 3 red fish.