Answer:
12
Step-by-step explanation:
Let x be the number of gallons of water in lake Mead.
Given that there is 326099 gallons in 1 acre-foot, we calculate Mead's gallons as:
[tex]1 acrefoot=326099g\\28945000acrefoot=x\\\\x=\frac{28945000acrefoot\times326099g}{1acrefoot}\\\\x=9.4\times 10^{12} \ gallons[/tex]
We now equate x to [tex]9.4\times10^a[/tex];
[tex]9.4\times 10^a=9.4\times 10^{12}\\\\a=12[/tex]
Hence, a=12
What is the measure of arc EG?
The measure of arc EG = 16°.
Solution:
Given data:
m∠X = 47° and m(ar FH = 110°)
To find the measure of arc EG:
We know that,
Angle formed by two intersecting secants outside the circle is equal to half of the difference between the intercepted arcs.
[tex]$m \angle X=\frac{1}{2}({arc} \ FH-{arc} \ EG)[/tex]
[tex]$47^{\circ}=\frac{1}{2}\left(110^\circ- {arc} \ EG}\right)[/tex]
Multiply by 2 on both sides.
94° = 110° - arc EG
Subtract 110° from both sides.
-16° = -arc EG
Multiply -1 on both sides, we get
16° = arc EG
Switch the sides.
arc EG = 16°
The measure of arc EG = 16°.
(Evaluate each logarithm. Use the change of base formula when necessary) helpppp y’all
The value of [tex]\log _{6}(36)[/tex] is 2.
Solution:
Given expression is [tex]\log _{6}(36)[/tex].
To evaluate the expression:
[tex]\log _{6}(36)[/tex]
36 can be written as 6².
[tex]=\log _{6}\left(6^{2}\right)[/tex]
Using log rule: [tex]\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)[/tex]
[tex]=2 \log _{6}(6)[/tex]
Using log rule: [tex]\log _{a}(a)=1[/tex] so that [tex]\log _{6}(6)=1[/tex]
= 2(1)
= 2
[tex]\log _{6}(36)=2[/tex]
Hence the value of [tex]\log _{6}(36)[/tex] is 2.
Final answer:
To find log₆ 36, we determine the exponent that 6 must be raised to to get 36. As 6 squared equals 36, the value of log base 6 of 36 is 2.
Explanation:
The question asks us to evaluate the logarithm of 36 with a base of 6, or, in mathematical terms, log base 6 of 36. We can solve this by recalling the definition of a logarithm, which is the power to which a base number must be raised to yield a given number. Since 6 squared is equal to 36 (6² = 36), the logarithm of 36 with a base of 6 is equal to 2.
Sigi’s taxi company charges $0.60 per mile and adds an additional $4.50 to cover the cost of bridge tolls. The expression below represents this relationship.
0.60m + 4.50
How much will the taxi company charge for a 36-mile drive?
a) $5.10
b) $26.10
c) $27.00
d) $41.10
Final answer:
To calculate the charge for a 36-mile drive by Sigi's taxi company, multiply 0.60 by 36 to find the mileage cost, add the $4.50 bridge toll, which results in a total cost of $26.10. Hence, the correct answer is (b) $26.10.
Explanation:
The question asks how much Sigi’s taxi company will charge for a 36-mile drive considering their rate is $0.60 per mile and there is an additional charge of $4.50 for bridge tolls. To calculate the total cost, you can use the given expression 0.60m + 4.50, where 'm' represents the number of miles.
By substituting 36 for 'm', you get the following calculation: 0.60 × 36 + 4.50. The cost per mile for 36 miles amounts to $21.60 ($0.60 times 36). Add the additional $4.50 charge for bridge tolls to get a total charge of $26.10.
Step-by-Step Calculation:
Calculate the cost of the mileage: 0.60 × 36 = $21.60.Add the fixed bridge toll cost: $21.60 + $4.50 = $26.10.Therefore, the correct option is (b) $26.10.
What is P (beaver)?
If necessary, round your answer to 2 decimal places
Answer:
Step-by-step explanation:
14/8
a die is rolled. What is the probability that the result is less than 3?
Answer:
⅓
Step-by-step explanation:
Less than 3: 1 or 2
2/6 = 1/3
What is the probability of getting an even number on the roll of a six-sided die? 1/6 1/3 1/2
Answer: 1/2
Step-by-step explanation:
The sample space when a six sided die is thrown once is :
{ 1,2,3,3,5,6}
The even numbers are :
{2,4,6}
Therefore :
P(even) = n(even) / total number
That is
P(even) = 3/6
P(even) = 1/2
A soccer field (football pitch) has a length of 103.2 m and a width of 71.5 m. Find the total area of the field in square meters (m2) and convert this measurement to square yards (yd2).
Answer:
The total area of the field is 7378.8 square meters.
The total area of the field is 8825.0448 square yards.
Step-by-step explanation:
Given : A soccer field (football pitch) has a length of 103.2 m and a width of 71.5 m.
To find : The total area of the field in square meters (m²) and convert this measurement to square yards (yd²) ?
Solution :
The length l=103.2 m
The width w=71.5 m
The area of the field is [tex]A=l\times w[/tex]
[tex]A=103.2\times 71.5[/tex]
[tex]A=7378.8\ m^2[/tex]
The total area of the field is 7378.8 square meters.
We know that,
1 m²= 1.196 yd²
[tex]7378.8\ m^2=7378.8\times 1.196\ yd^2[/tex]
[tex]7378.8\ m^2=8825.0448\ yd^2[/tex]
The total area of the field is 8825.0448 square yards.
The area of the soccer field is 7378.8 m^2 and 8822.6 square yards.
Explanation:The area of a rectangle (which is the shape of a soccer field) can be found by multiplying the length and the width. So, the area of the soccer field in square meters is 103.2 m (length) times 71.5 m (width), which equals 7378.8 m2.
To convert this area to square yards, you should know that 1 square meter is approximately equal to 1.19599 square yards. So, multiply our previous answer with this value. The area of the soccer field will be 7378.8 m2 times 1.19599 to get 8822.6 yd2.
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A regular hexagon has sides measuring
7 inches. If the hexagon is divided into 6
congruent triangles, each has a height of
about 6 inches. What is the approximate
area of the hexagon?
Explain please!
Answer:
Approximately 252 inches squared.
Step-by-step explanation:
Answer:
126 in.^2
Step-by-step explanation:
The hexagon is divided into 6 congruent triangles. The area of the hexagon is 6 times the area of one of the triangles.
Now think of each triangle.
The side of the hexagon is the base of the triangle. The side of the hexagon has length 7 inches, so the base of the triangle has length 7 inches.
The height of the triangle is approximately 6 inches.
area of triangle = base * height/2
area of hexagon = 6 * area of triangle
area of hexagon = 6 * base * height/2
area of hexagon = 3 * base * height
area of hexagon = 3 * 7 in. * 6 in.
area of hexagon = 126 in.^2
in a triangle ABC, mA=45, mB 40, and a=7. which equation sould you solve to find B?
Answer:
[tex]\frac{sin(45^o)}{7}=\frac{sin(40^o)}{b}[/tex]
Step-by-step explanation:
The correct question is
In a triangle ABC, m∠A=45°, m∠B 40°, and a=7. which equation should you solve to find b?
we know that
Applying the law of sines
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}[/tex]
substitute the given values
[tex]\frac{sin(45^o)}{7}=\frac{sin(40^o)}{b}[/tex]
solve for b
[tex]b=(7)sin(40^o)/sin(45^o)[/tex]
[tex]b=6.4\ units[/tex]
Answer:
Sin45/7 = sin40/b
Step-by-step explanation:
:D
33. Calista earns $300 per week for a 40 hour work week plus $12.32 per hour for each hour of
overtime after 40 hours. Write an equation that would be used to determine her weekly wages
where w is her wages, and v is the number of overtime hours worked.
Answer:
w = 300 +12.32v
Step-by-step explanation:
Calista's wages are ...
wages = (straight time earnings) + (overtime pay)
= $300 + (overtime hours)·(overtime pay per hour)
= $300 + (v)($12.32)
Using the symbols required by the problem statement, we have ...
w = 300 + 12.32v
Plzzz help me I don’t understand aTT ALL if I don’t do it I’ll get a 0 in my report card plz help
Answer:
hi there! i can help you out! i don't want you to get a zero on your report card!!
Step-by-step explanation:
so, on the x-axis, which is all the numbers through 1-10 and there are the patient's number. so for ex, the first question says patient 1 : 3 hours right??
so the hours are the y-axis and you can label them 2,4,6,8 because skip counting by twos are probably the easiest! so for the first question, you would line a dot up on top of 1 and go up and you see 2 and 4 right, cuz you just labeled it... do go between 2 and 4 which is 3 and place the dot there...
and keep doing the same things with other ones too...
another ex! so on the second question, it says patient 2 : 7 hours so place the dot on top of the 2 and go up untill you see 6 and 8 and place the dot beween them!
Sorry but I forgot about Mean Median And Mode! Sorry I would hate to see you get a zero!
−x+4y=−9
y=−2x+6
Is (2,3)(2,3)left parenthesis, 2, comma, 3, right parenthesis a solution of the system?
The solution of the equation 4y − x + 9 = 0 and y = 6 − 2x will be (11/3, −4/3). Point (2, 3) is not the solution of the system.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equations are given below.
−x + 4y = −9 ...1
y = −2x + 6 ...2
From equations 1 and 2, then we have
−x + 4(−2x + 6) = −9
−x − 8x + 24 = −9
−9x + 24 = −9
9x = 24 + 9
9x = 33
x = 11 / 3
Then the value of the variable 'y' is calculated as,
y = −2(11/3) + 6
y = −22/3 + 6
y = −4/3
The arrangement of the situation 4y − x + 9 = 0 and y = 6 − 2x will be (11/3, −4/3). Point (2, 3) isn't the arrangement of the framework.
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The point (2, 3) does not satisfy either of the given equations, −x + 4y = −9 and y = −2x + 6. Therefore, it is not a solution to the system of equations.
Explanation:To determine if the point (2, 3) is a solution to the system of equations consisting of −x + 4y = −9 and y = −2x + 6, we need to check whether the point satisfies both equations.
For the first equation, substitute x with 2 and y with 3: −(2) + 4(3) = −9 to see if it results in a true statement.For the second equation, substitute x with 2: −2(2) + 6 = 3 to see if it equates to the y-value of 3.
Let's substitute the values into the first equation:
−(2) + 4(3) = −8 + 12 = 4, which does not equal −9. Therefore, the point does not satisfy the first equation.
For the second equation:
−2(2) + 6 = −4 + 6 = 2, which does not equal 3. Hence, the point does not satisfy the second equation either.
Since the point (2, 3) does not satisfy either equation, it is not a solution to the system of equations.
Anthony would like to estimate how many books he reads per week on average. For
six weeks, he has been producing a list of the books he had just read. His results are
given in the table. Assuming that these six weeks are representative of his reading
habits, what is the average number of books does Anthony read per week?
Week 1 2 3 4 5 6
Numbers of Books 2 3 1 2 0 1
O 1.5
O 1.8
03
O 0.67
Answer:
The correct answer is A. 1.5
Step-by-step explanation:
This is the information given to us to answer the question correctly:
Week 1 2 3 4 5 6
Numbers of Books 2 3 1 2 0 1
**************************************************
Assuming that these six weeks are representative of his reading habits, what is the average number of books does Anthony read per week?
Let's calculate the average number of books, this way:
Average number of books Anthony reads per week = (2 + 3 + 1 + 2 + 0 + 1)/6
Average number of books Anthony reads per week = 9/6
Average number of books Anthony reads per week = 1.5
The correct answer is A. 1.5
Hey can someone answer this for me
y = 75
Solution:
In a straight line, sum of the adjacent angles = 180°
80° + m∠DGF = 180°
Subtract 80° from both sides of the equation.
m∠DGF = 100°
Sum of all the interior angles in a quadrilateral = 360°
m∠DGF + m∠GFE + m∠FED + m∠EDG = 360°
100° + 120° + 65° + y° = 360°
285° + y° = 360°
Subtract 285° from both sides, we get
y° = 75°
Hence the value of y is 75.
A triangular banner has a base length of 48
inches. The banner has an area of 1,632 square
inches. What is the height of the banner?
Answer:68
Step-by-step explanation:
Area of triangle=1/2×base×height
1632=1/2×48×h
1632×2=48×h
3264=48×h
3264/48=h
68=h
Final answer:
To find the height of a triangle with an area of 1,632 square inches and a base of 48 inches, we use the formula A = (base × height) / 2. Solving for height gives us a result of 68 inches.
Explanation:
To calculate the height of a triangle when its area and base length are known, we use the formula for the area of a triangle: A = (base × height) / 2. Given that the area of the triangular banner is 1,632 square inches and the base length is 48 inches, we can set up the equation:
1,632 = (48 × height) / 2
Multiplying both sides of the equation by 2 to get rid of the denominator:
3,264 = 48 × height
Next, divide both sides by 48 to isolate the height:
height = 3,264 / 48
height = 68 inches
Therefore, the height of the triangular banner is 68 inches.
which best describes the triangle or triangles, if any that can be formed with two sides that each measure 5 inches and an angle that measures 60 degrees?
Answer: D. one equilateral triangle
explanation: Means, triangle is equilateral. If angle between , two sides having measure 5 cm , is not 60 degree, then the triangle will be always Isosceles. we will sine rule to find remaining measurements. In this case,also ,triangle is equilateral
Answer: one equilateral triangle
Step-by-step explanation:
7x +39 > 53
AND
16x + 15 > 31
Answer:
x > 2
Step-by-step explanation:
7x +39 > 53
AND
16x + 15 > 31
7x > 14
AND
16x > 16
x > 2
AND
x > 1
And is intersection, which is x > 2
Select the correct answer.
For Bracken to break even (suffer no loss and earn no profit) over the passage of 3 years, about how many claims for surgical procedures can the 1,000 insured people file?
A. 1,000
B. 900.
C.90
D. 18
E. 180
Answer: 900
Step-by-step explanation:
Answer:
900
Step-by-step explanation:
Identify the like terms.
-4a, -3b, 4b, 3
A -4a and 4b
B -3b and 3
C -3b and 4b
D -4a and -3b
Answer:
C
Step-by-step explanation:
Answer:c
Step-by-step explanation:
Write the equation of the line that passes through the point (-5,5) and has a slope of -8/5
A) y= -8/5 x - 3
B) y= -8/5x+3
C) 3x - 5y =0
D) 5x-3y=0
Answer:
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=\frac{-8}{5}x-3[/tex]
Step-by-step explanation:
Given the point (-5, 5)
slope = m = -8/5
Using the slope intercept form:
[tex]y=mx+b[/tex]
Plugging point (-5, 5) and slope = m = -8/5 in the slope intercept form to find the y-intercept 'b'.
[tex]5=\frac{-8}{5}\left(-5\right)+b[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]\frac{-8}{5}\left(-5\right)+b=5[/tex]
[tex]8+b=5[/tex]
[tex]8+b-8=5-8[/tex]
[tex]b=-3[/tex]
so the equation of the line will be:
[tex]y=mx+b[/tex]
plugging m = -8/5 and b = -3 in slope intercept form
[tex]y=\frac{-8}{5}x-3[/tex]
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=\frac{-8}{5}x-3[/tex]
The question is in the picture
PLEASE HURRY!!!!
Answer:
1, 3, 5
Step-by-step explanation:
Answer:
A, C, and E
Step-by-step explanation:
Explanation for A.) 25 x the number of shirts has to be less than 300 and this means 25s < 300
Explanation for C.) Divide both sides by 25 which turns it into s < 12. < = open circle.
Explanation for E.) The value of s is less than the value of 12 which means the arrow points left.
Consider circle C below where the central angle is measured in radians
Answer: 12 units
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
ed 2020
Which number from the set {0, 2, 3, 5} is the solution to this equation?
5x − 4 = 3x + 6
A) 0
B) 2
C) 3
D) 5
Answer:
The answer is D: 5
Step-by-step explanation:
5 x 5 = 25 - 4 = 21 and 3 x 5 = 15 + 6 = 21
Answer: 5
Step-by-step explanation: Here, we want to determine which number can be replaced for the variable in this problem so the statement holds true.
5 would be the only number in this set that can work. Let's test it out.
We can do this by simply plugging in 5 for x. If the statement holds true when 5 is plugged in for x, then 5 is a solution.
Plugging in 5 for x, we have 5(5) - 4 = 3(5) + 6.
Simplifying, we have 25 - 4 = 15 + 6 or 21 = 21 which is a true statement.
So 5 is a solution.
Graph this line using the slope and y-intercept Y=1/2x+9
Answer:
Step-by-step explanation:
I don't have a picture so I'll visually describe it. You start at the point (0,9) because 9 is the y intercept. Now that you have your first point, to get the next point, move up one and 2 to the right. Now, you're at the point (2,10). Continue going up one and 2 to the right until you get to the end of the graph. Then, go back to the point (0,9). This time, go the opposite way. Go one down, and two to the left. Now, you should be at the point (-2,8). Continue going down one, two left until once again, you run out of room on the graph. Then, use a ruler or freehand draw a line connecting your points. Add arrows on the ends on the line. Hope this helped!
Charles opened a door hinged at O by an angle of 45 degrees. The width of the door was 80 centimeters. Find the area swept by the door. Leave your answer in terms of pie
Answer:
A=800πcm²
Step-by-step explanation:
Knowing that the area of a circular sector is:
[tex]A_{cs}=\frac{\pi\alpha r^{2}}{360}[/tex]
where α is the sweep angle and r in the radio (according to the graph),
then
A=(45° π 80²)/360° = 800πcm²
Final answer:
The area swept by the door is 10π cm and the area of the sector is 200π cm².
Explanation:
To find the area swept by the door, we can first find the length of the arc created by the door when it opens. The arc length formula is given by:
Arc length = r × θ
Where r is the radius (half the width of the door) and θ is the angle through which the door opens. In this case, the radius is 40 centimeters (half of 80 centimeters) and the angle is 45 degrees.
So, the arc length = 40 cm × (45 degrees) = 40π/4 cm = 10π cm
The swept area can be approximated by treating it as a sector of a circle with radius 40 cm and central angle 45 degrees. The area of the sector is given by:
Area = (θ/360) × π × r²
Where θ is the central angle and r is the radius. Substituting the values, we get:
Area = (45/360) × π × (40 cm)² = 1/8 × π × 1600 cm² = 200π cm²
Find the surface area of the present.
cm2
20 cm
20 cm
-
20 cm
The surface area of the present in the shape of a cube is 2,400 square centimeters.
The present takes the shape of a cube.
The formula for the surface area of a cube is expressed as:
Surface area = 6( a² )
Where a is the edge length.
From the figure, the edge length of the present is;
Edge length a = 20cm
Surface area =?
To determine the surface area of the present, plug the given value into the above formula:
Surface area = 6( a² )
Surface area = 6( 20² )
Surface area = 6( 400 )
Surface area = 2,400 cm²
Therefore, the surface area measures 2,400 cm².
This question is not complete, the complete question is:
The present shown below is a cube.
Find the surface area of the present.
Wat does f(x)=x^2+x-30 solve to?
Answer:
F(X) = 5 or -6
Step-by-step explanation:
F(X) = [tex]x^{2} +x-30[/tex]
Using the Formula
[tex]-b[/tex]±[tex]\frac{\sqrt{b^{2} -4ac } }{2a}[/tex]
Where a = coefficient of [tex]x^{2}[/tex] i. e 1
b = coefficient of [tex]x[/tex] i. e 1
And c = 30
imputing the values, we have
[tex]-1[/tex] ± [tex]\frac{\sqrt{1^{2} - 4 X 1 X 30} }{2 X 1}[/tex]
[tex]-1[/tex] ± [tex]\frac{\sqrt{121} }{2}[/tex]
[tex]-1+\frac{11}{2}[/tex] OR [tex]-1-\frac{11}{2}[/tex]
Therefore, F(X) is either 5 or -6
When is a lower annual interest rate better than a low annual fee?
Answer:
Lower annual interest in real terms is a relief to customers because it can go across a monthly payment like in a product purchase with a credit card. A low annual fee is just one payment that can be a certain membership of which happens only on an annual basis.
Answer:
Lower annual interest in real terms is a relief to customers because it can go across a monthly payment like in a product purchase with a credit card. A low annual fee is just one payment that can be a certain membership of which happens only on an annual basis.
Step-by-step explanation:
edge
There are 7 spiders in the barn. Each spider has 8 legs. How many legs do the spiders have altoghther
Answer:
56
Step-by-step explanation:
Answer:
56 legs
Step-by-step explanation:
Because each spider has 8 legs and there are 7 spiders in all, you must find the product of 8x7. This is just a simple multiplication problem, so 8 multiplied by 7 is 56.
The rectangle below has an area of 121-x^2121−x
2
121, minus, x, squared square meters and a length of 11-x11−x11, minus, x meters.
What expression represents the width of the rectangle?
The width of the rectangle can be represented by the expression (121-x^2) / (11-x).
Explanation:To find the width of the rectangle, we need to divide the area of the rectangle by its length. The area of the rectangle is given by the expression 121-x^2, and the length is given by 11-x. So, we can represent the width as:
Width = (Area / Length) = (121-x^2) / (11-x)
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