Answer:
24.4
Step-by-step explanation:
diameter=2*radius
=2*12.2
=24.4
Final answer:
The diameter of a circle with a radius of 12.2 is 24.4 units. This is calculated by doubling the radius, using the formula D = 2r.
Explanation:
To determine the diameter of a circle with a radius of 12.2, you simply need to use the relationship between the radius and the diameter of a circle. The diameter is twice the radius, which can be represented by the formula D = 2r, where D is the diameter and r is the radius.
Substituting the value of the radius into the formula gives us:
D = 2 × 12.2
This calculates to:
D = 24.4
Therefore, the diameter of the circle is 24.4 units. Keep in mind that if the radius was given in a specific unit, like meters or centimeters, then the diameter will be in the same unit.
Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 5% syrup?
4.75 lbs of water and 0.25 lbs of sugar is needed to make 5% of syrup.
Solution:
Let us assume that x is the required pounds sugar to make 5% syrup
[tex]\Rightarrow\frac{x}{\text{total quantity}}=5\%[/tex]
which is [tex]\frac{x}{5}=5\%[/tex]
On solving we get,
[tex]\Rightarrow\frac{x}{5} =0.05 [5\%=\frac{5}{100}][/tex]
[tex]\Rightarrow x = 5\times0.05\rightarrow x=0.25[/tex]
If the required sugar to make 5% syrup is 0.25 lbs then the remaining quantity in the total sugar syrup would be water. That is,
[tex]5 \text{ lbs }-0.25 \text{ lbs }=4.75 \text{ lbs }[/tex]
So, the required amount is 0.25 lbs of sugar and 4.75 lbs of water.
Answer:
4.75 lbs of water and 0.25 lbs of sugar is needed to make 5% of syrup.
Solution:
Let us assume that x is the required pounds sugar to make 5% syrup
which is
On solving we get,
If the required sugar to make 5% syrup is 0.25 lbs then the remaining quantity in the total sugar syrup would be water. That is,
So, the required amount is 0.25 lbs of sugar and 4.75 lbs of water.
Step-by-step explanation:
Consider the diagram shown. Choose all the true statements.
If Θ = 2 rad, then r > s.
If Θ = 1 rad, then r ≤ s.
If s = 1/2r, then 2Θ = 1.
If s/2r=1, then Θ = 2
Answer:
If Θ = 1 rad, then r ≤ s
If s = 1/2r, then 2Θ = 1
If s/(2r)=1, then Θ = 2
Step-by-step explanation:
we know that
The arc length s is equal to
[tex]s=r\theta[/tex]
where
r is the radius
[tex]\theta[/tex] is the central angle in radians
Verify each statement
case 1) If Θ = 2 rad, then r > s
The statement is false
Because
For Θ = 2 rad
substitute
[tex]s=r(2)\\s=2r[/tex]
so
[tex]s>r[/tex]
case 2) If Θ = 1 rad, then r ≤ s
The statement is true
Because
For Θ = 1 rad
substitute
[tex]s=r(1)[/tex]
[tex]s=r[/tex]
so
[tex]r\leq s[/tex] ---> is true
case 3) If s = 1/2r, then 2Θ = 1
The statement is true
Because
For s=1/2r
substitute
[tex]\frac{1}{2}r=r\theta[/tex]
[tex]\theta=\frac{1}{2}[/tex]
[tex]2\theta=1[/tex]
case 4) If s/2r=1, then Θ = 2
The statement is true
Because
For Θ = 2
substitute
[tex]s=r(2)\\\\\frac{s}{2r}=1[/tex]
What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 5. Base C B is labeled as 6. Segment A D is labeled as x. Segment B D is labeled as 4.2.
Answer:
The correct answer is indeed 3.5 :)
Step-by-step explanation:
just took the test <3 hopes this help
The value of x is 3.5.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Right triangle with vertices labeled as A, B, and C.
Side C B is the base and the top vertex is A.
Side A B contains a midpoint D.
A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D.
Side A C= 5.
Base C B = 6.
Line Segment A D = x.
Segment B D=4.2.
4.2/6=x/5
Apply cross multiplication
4.2×5=6x
21=6x
Divide both sides by 6
x=3.5
Hence, the value of x is 3.5.
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Excellent! Move on to the 7th (or 8th if you count 0)
Fibonacci number.
Answer:
The answer is 13 if you count 0.
Step-by-step explanation:
The sequence is as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
Also, have a great day and Happy Valentines! <3
How many solutions in the equation y=x-3 and 4x-10y=6
Answer:
1
Step-by-step explanation:
These are two lines with different slopes and y intercepts so they will intersect once
Final answer:
Explaining how to find the number of solutions in a system of linear equations.
Explanation:
The given equations are:
y = x - 3
4x - 10y = 6
To find the number of solutions, we can solve these equations simultaneously.
Substitute y = x - 3 into the second equation and solve for x to find the value of y. If the solution leads to a valid pair of x and y that satisfies both equations, then there is one unique solution, otherwise there are no solutions.
Can you guys help me??? 6 = -5 + u. What is u???
Work is provided in the image attached.
When multiplying the fractions 1/6 and 7/8 what is the product of the numerators?
Answer:
Step-by-step explanation:
1 7 7 <== numerator
-------- X ------ = --------
6 8 48 <== denominator
" the product " is the result of multiplying
so the product of the numerators is 7
The product of the numerators is 7.
What is Fraction?All fragments correspond of a numerator and a denominator and they're separated by a vertical bar known as the fractional bar.
The denominator indicates the number of corridor in which the total has been divided into. It's placed in the lower part of the bit below the fractional bar.The numerator indicates how numerous sections of the bit are represented or named. It's placed in the upper part of the bit above the fractional bar.Given:
We have have to multiply the fraction 1/6 to 7/8.
First, the product of Numerator
1 x 7 = 7
and, product of Denominator
6 x 8 = 48
Thus, the product of the numerators is 7.
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Substitute -1 for y into the second equation for the example do you still get X equals negative 4
Answer:
you need to give more information for a good answer
Which inequality is true?
A number line going from negative 1 to 1.
One-half less-than one-third
Three-fourths greater-than two-thirds
Negative one-fourth less-than negative two-thirds
Negative 1 greater-than three-fourths
Option C: Three-fourths greater-than two-thirds
Solution:
Option A: A number line going from negative 1 to 1.
Explanation: A number line is used to define a point in a given interval. And hence, a number line does not goes from negative 1 to 1.
Thus, this statement is false.
Option B: One-half less-than one-third
Explanation: The statement can be written as
[tex]\begin{array}{c}{\frac{1}{5}<\frac{1}{3}} \\{0.5<0.33}\end{array}[/tex]
which is not possible.
Hence, this inequality is false.
Option C: Three-fourths greater-than two-thirds
Explanation: The statement can be written as
[tex]\begin{array}{c}{\frac{3}{4}>\frac{2}{3}} \\{0.75>0.667}\end{array}[/tex]
which is true.
Hence, this inequality is true.
Option D: Negative one-fourth less-than negative two-thirds
Explanation: The statement can be written as
[tex]\begin{aligned}-\frac{1}{4} &<-\frac{2}{3} \\-0.25 &<-0.667\end{aligned}[/tex]
This is not possible.
Hence, this inequality is false.
Option E: Negative 1 greater-than three-fourths
Explanation: The statement can be written as
[tex]\begin{array}{l}{-1>\frac{3}{4}} \\{-1>0.75}\end{array}[/tex]
This is not possible.
Hence, this inequality is false.
Answer:
the person who answered this question is actually correct she just put option c when its actually option d people make mistakes its okay thats how u learn
Step-by-step explanation:
In 15 and 16, use the expression 1 + z/3 + 2w
15) Which part of the expression is a quotient? DESCRIBE its parts.
16) Which part of the expression is a product of two factors? DESCRIBE its parts.
We want to analyze the terms of the given expression.
15) second term, z/3
16) third term, 2*w
The given expression is:
1 + z/3 + 2*w
15) We want to find which part of the expression is a quotient.
A general quotient is something of the form a/b, so compared with the expression, the term that is a quotient is the second term; z/3.
Where the first number, z, is called the numerator and the second is called the denominator.
Notice that the variable z is on the numerator, so this would be a linear dependence with z.
16) We want to find which part of the expression is a product of two factors.
It is the third term, 2*w
Where the two factors are 2 and w.
Again, the variable si w, and we are multiplying it by a constant number, 2.
So we also have a linear dependence with w.
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In the expression 1 + z/3 + 2w, the quotient is z/3, where z is the numerator and 3 is the denominator. The product of two factors is 2w, with 2 and w being the factors.
Explanation:The student asked about parts of the expression 1 + z/3 + 2w.
15) Quotient in the Expression
The quotient refers to the result of division. In the expression given, the quotient is z/3. Its parts are the numerator z, which is the value being divided, and the denominator 3, which is the value by which z is divided.
16) Product of Two Factors in the Expression
The product refers to the result of multiplication. In the expression, the product is 2w. Its parts are the two factors being multiplied: the constant 2 and the variable w.
a number c increased 6 by is less than or equal to -26
Answer:
[tex]c\leq -32[/tex]
Step-by-step explanation:
Let
c ---> the number
we know that
The number c plus 6 must be less than or equal to -26
so
The inequality that represent this situation is
[tex]c+6\leq -26[/tex]
Solve for c
Subtract 6 both sides
[tex]c\leq -26-6[/tex]
[tex]c\leq -32[/tex]
The solution for c is the interval (-∞,-32]
All real numbers less than or equal to -32
In a number line, the solution is the shaded area at left of c=-32 (closed circle)
see the attached figure to better understand the problem
3x + 7y = -5
8x + 9y = 6
The question involves solving simultaneous linear equations, a high school level topic in mathematics. Methods like substitution or elimination can be used to find the values of the variables.
The student's question involves solving simultaneous linear equations, which is a topic in mathematics. To solve the given system of equations, one can use methods such as substitution, elimination, or matrix operations like determinants. The elimination method can be particularly efficient. For example, you can multiply the first equation by a number that will allow the x or y terms to cancel out when added or subtracted from the second equation. After simplifying, you're left with one equation in one unknown, which can be easily solved. Then, back-substitute the known value into one of the original equations to solve for the other variable.
Given the equations 3x + 7y = -5 and 8x + 9y = 6, we may choose to multiply the first equation by 3 and the second by 7 (to eliminate the x terms) or to multiply the first equation by 8 and the second by 3 (to eliminate the y terms). Once one variable is eliminated, we solve for the other and use it to find the value of the remaining variable.
vimesha drove 232 miles in 4 hours. at this rate, how far could she drive in 7 hours? what is her rate of speed in miles per hour?
Answer: distance = 406 miles
speed = 58 miles/hr
Step-by-step explanation:
4 hours - 232 miles
1 hr - 232/4
7 hours - 232/ 4 x 7 = 406 miles
Therefore , her distance is 406 miles for 7 hours.
Speed = distance / time
speed = 406/7 = 58 miles/hr
Which expression is equivalent to the expression 5(3x+4-x)
Final answer:
The equivalent expression to 5(3x+4-x) is obtained by combining like terms and distributing the 5, which results in 10x + 20.
Explanation:
To find an expression equivalent to 5(3x+4-x), we must first simplify the expression inside the parentheses. We combine like terms 3x and -x, which gives us 2x. Then, we distribute the 5 across the simplified expression within the parentheses:
5(3x+4-x) = 5(2x+4) = 5*2x + 5*4 = 10x + 20.
So the expression equivalent to 5(3x+4-x) is 10x + 20. This process involves simplifying expressions step by step, ensuring clarity and accuracy in mathematical computations. By systematically combining like terms and distributing constants, we obtain a concise and equivalent expression that represents the original expression's value.
Liz earns a salary of $2,200 per month, plus a commission of 3% of her sales. She wants to earn at least $2,800 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.
Answer:
The amount of sales in order to meet her goal must be greater than or equal to $20,000
Step-by-step explanation:
Let
x----> represent the amount of sales Liz will need
we know that
The amount of sales for the month multiplied by the commission rate as a decimal plus the fixed amount must be greater than or equal to $2,800 each month
so
The inequality that represent this situation is
[tex]0.03x+2,200\geq 2,800[/tex]
solve for x
subtract 2,200 both sides
[tex]0.03x \geq 2,800-2,200[/tex]
[tex]0.03x \geq 600[/tex]
divide by 0.03 both sides
[tex]x \geq \$20,000[/tex]
The amount of sales in order to meet her goal must be greater than or equal to $20,000
theresa has two brothers , paul and Steve, who are both the same height. Paul says he is 16 inches shorter then 1 1/2 times theresas height. Steve says he is 6 inches shorter then 1 1/3 times theresas height. if they are both right how tall is Theresa? write an expression to represent Pauls height in inches
Answer:
7ft
Step-by-step explanation:
p=paul's height
s=steve's height
t=theresa's height
p=s
1 and 1/2=3/2
1 and 1/3=4/3
p=-16+(3/2)t
s=-6+(4/3)t
p=s so
-16+(3/2)t=-6+(4/3)t
add 6 to both sides
-10+(3/2)t=(4/3)t
times both sides by 6 to clear fractions
-60+9t=8t
minus 9t both sides
-60=-t
times -1
60=t
t=60
theresa is 60 inches or 5ft
steve and paul are 84 inches or 7ft (wow!)
Mr. Phillips is mixing paint for his art
class. How many 6-ounce bottles can
he fill with the quantities of paint shown
at the right? Explain.
Answer:
the question lacks the full information and is incomplete.
Step-by-step explanation:
The radius of a circle is 4 millimeters. What is the circle's circumference?
Will give brainiest
Answer:25.12
Step-by-step explanation:
-99 less than a number
Answer:
-99 is less than -98
-99 is less than -97
-99 is less than -96
.
.
.
-99 is less than -1
-99 is less than 0
-99 is less than (any posifive number)
What is a mean median and mode
Answer:
Mean, median, and mode are three kinds of "averages".
Step-by-step explanation:
Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
The mean is the usual average, so I'll add and then divide:
(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15
Note that the mean, in this case, isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.
The median is the middle value, so first I'll have to rewrite the list in numerical order:
13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:
13, 13, 13, 13, 14, 14, 16, 18, 21
So the median is 14.
The mode is the number that is repeated more often than any other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.
mean: 15
median: 14
mode: 13
range: 8
Final answer:
Mean, median, and mode are basic statistical measures used to find the center of a data set. Mean finds the average, median identifies the middle value when data is ordered, and mode determines the most frequently occurring value.
Explanation:
Mean, median, and mode are measures of central tendency that describe the way in which different values cluster around a central point in a set of data.
The mean is the average of all the numbers in the data set. You calculate the mean by adding up all the numbers and dividing by the total number of values.
The median is the middle value of an ordered data set. If the data set has an odd number of values, the median is the exact middle number. If there is an even number of values, the median is the average of the two central numbers.
The mode is the value that appears most frequently in the data set. If no number repeats, the data set has no mode; if two or more numbers occur with equal frequency and more often than any other number, the dataset is multimodal, having several modes.
Each of these measures provides a different perspective on the typical value or center of a dataset, and is useful in various statistical analyses.
2x-y=-1 in slope intercept form
Answer:
y = 2x + 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of a line in a standard form.
Convert to the slope-intercept form:
[tex]2x-y=-1[/tex] add y to both sides
[tex]2x-y+y=-1+y[/tex]
[tex]2x=-1+y[/tex] add 1 to both sides
[tex]2x+1=-1+1+y[/tex]
[tex]2x+1=y\to y=2x+1[/tex]
The slope intercept form of the given equation is y = 2x+1
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
(ii) 3x + 5 = 15
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given that, an equation of a line, 2x-y = -1, we need to convert this into slope intercept form,
The standard form of the equation of a line in slope intercept form, is given by :
y = mx+c
Where, m = slope of the line, c is the y-intercept,
So, the given equation is 2x-y = -1,
Add y both the side,
2x-y+y = -1+y
2x = -1+y
Add 1 in both sides,
2x+1 = y+1-1
y = 2x+1
Hence, the slope intercept form of the given equation is y = 2x+1
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Please answer asap! will mark brainliest!
Describe the solution of f(x) shown in the graph
a parabola opening up passing through 0 comma 2, 1 comma zero and 2 comma zero
All real solutions is the answer
At a sale on winter clothing Cody brought two pairs of gloves and four hats for $43.00 tori bought two pairs of gloves and two hats for 30.00.find the prices of the hats and gloves
Answer:
Cost of one glove pair is $ 8.50 and the cost of one hat is $6.50
Step-by-step explanation:
Let g represents the cost of one gloves pair
h represents the cost of one hat
Then
Cody brought two pairs of gloves and four hats for $43.00
This can be written as
2g + 4h = 43-------------------(1)
Tori bought two pairs of gloves and two hats for 30.00
This can be written as
2g + 2h = 30------------------(2)
Subtracting (2) from (1)
2g + 4h = 43
2g + 2h = 30
(-)
--------------------------
0g + 2h = 13
------------------------------------
2h =13
h = 13 / 2
h = 6.5---------------------(3)
Substituting (3) in (2)
2g + 2(6.5) = 30
2g + 13 = 30
2g = 17
g = 17 / 2
g = 8.5
So one hat is $6.50 and one pair of gloves is $8.50.
What are the measures of the two angles in the figure? A. 125° and 55° B. 120° and 60° C. 100° and 80° D. 92° and 88°
Step-by-step explanation:
Know that the sum of angle A & B equal 180°In order to find the measures you must find X. Plug X's value into the equations for angle A and Bboth should equal 180°Answer:
Step-by-step explanation: You would do 5x+20+x+40=180
Then you would add 5x and x together and you would also add 20 and 40 together and then you get: 6x+60=180
You would then subtract 180-60 and then you should get 6x=120 and the you would divide from both sides and you should get x=20 you would then plug it into both angles So 5(20)+20 and you should get 120 for the left angle and then you would do the next angle which would be 20+40=60 for the right angle
Short version:
5x+20+x+40=180
6x+60=180
6x=120
X=20
Which of the following representations are functions?
A only
A and B only
A and C only
A, B and C
Option 2: A and B only
Step-by-step explanation:
A: [tex]\{(0,9),(3,12),(-5,10),(5,10)\}[/tex]
The function can be represented in ordered pairs. Also, the x-values are not repeated and each has only one y-value. Hence, in this given ordered pair the values of x are not repeated and each has only one y-value.
Thus, A is a function.
B: [tex]y=x^{2} +10[/tex]
This is the general way of representing a function in which the input value (x-value) exactly related to one output value (y-value). Hence, in this given function the x-value has only one y-value.
Thus, B is a function.
C: The function can also be represented using tables in which each x-value is not repeated and has only one y-value. But, in this given table, the values of x (x=10) are repeated twice.
Thus, C is not a function.
Option 1: A only
Reason: A and B are the correct representations of the function.
This option 1 is not the correct answer.
Option 2: A and B only
Reason: A and B are the correct representations of the function.
This option 2 is the correct answer.
Option 3: A and C only
Reason: C is not a function. Only A and B are the correct representations of the function.
This option 3 is not the correct answer.
Option 4: A, B and C
Reason: Only A and B are the correct representations of the function and C is not a function.
This option 4 is not the correct answer.
In the function f(x) = 6x + b, what must be the value of b, if f(5) = 1?
=============================================
Work Shown:
f(x) = 6x + b
f(5) = 6(5) + b .... replace every x with 5
f(5) = 30 + b
1 = 30 + b ..... replace f(5) with 1, since f(5) = 1 was given.
1-30 = 30 + b - 30 .... subtract 30 from both sides
-29 = b
b = -29
-----------
The function f(x) = 6x+b turns into f(x) = 6x+(-29) which is equivalent to f(x) = 6x-29
Plugging in x = 5 leads to
f(x) = 6x-29
f(5) = 6(5) - 29
f(5) = 30 - 29
f(5) = 1
So we have confirmed the answer.
Answer:
Step-by-step explanation:
f(5) = 1
6*5 + b = 1
30 + b = 1
b = 1 - 30 = -29
b = -29
A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?
Area of the doghouse =- 32.5 sq. ft
Solution:
Given height = 5 ft, base1, [tex]b_1[/tex] = 5ft
Base2, [tex]b_2[/tex] = [tex]b_1+3=5+3=8[/tex] ft
Area of the trapezoid = [tex]\frac{1}{2}\times height\times (base1 +base2)[/tex]
[tex]=\frac{1}{2}\times 5\times (5+8)[/tex]
[tex]=\frac{1}{2}\times 5\times 13[/tex]
[tex]=\frac{1}{2}\times 65[/tex]
[tex]=32.5[/tex] sq. ft
Area of the trapezoid = 32.5 sq.ft
Hence the area of the doghouse is 32.5 sq. ft.
A brand of crackers is sold in a box shaped like a rectangular prism. The box has a length of 13 cm, a width of 8 cm, and a height of 22 cm. What is the volume of the box of crackers?
Answer:
LxWxH
Step-by-step explanation:
Volume can be calculated by using the formula: (length) x (width) x (height)
In this particular question, you are given the length as 13cm, the width as 8cm, and the height of 22cm.
To obtain the volume, you should plug these numbers into the formula (length) x (width) x (height)
When plugged in, the equation should look like this: (13cm) x (8cm) x (22cm).
When 13 x 8 x 22 =2288cm
Since you are calculating the volume, the answer will be given in centimeters cubed, so your final answer will be 2,288cm^3
Hope this explanation helps :)
Answer:
I think the answer is 2288 cm
In order to find volume of a rectangular prism you have to do l x w x h (length times width times height)
13 x 8 = 104
104 x 22 = 2288
I hope its right sorry if nott:(
Step-by-step explanation:
Write an inequality for x that would give this rectangle a perimeter of at least 300ft
Answer:
[tex] x\geqslant 300[/tex]
x is greater then or equal to 300
Solve the equation for x.
8(4x + 8) = 160
A) 3
B) 7
C) 12
D) 14
Answer:
Step-by-step explanation:
8(4x + 8) = 160.....distribute the 8 thru the parenthesis
8(4x) + 8(8) = 160
32x + 64 = 160....subtract 64 from both sides
32x + 64- 64 = 160 - 64
32x = 96
x = 96/32
x = 3 <===