The number of hours Matt babysits his sister is 1 and half hours.
Given that, Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip.
Let the number of half an hours Matt babysits his sister be x.
Matt made $18.50
So, equation is 5.50x+2 =18.50
5.50x=16.50
x=16.50/5.50
x= 3
Which means 1 and half hours he babysits his sister.
Therefore, the number of hours Matt babysits his sister is 1 and half hours.
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Show that the circles touch each other internally.
This shows that the two circles intersect at a point P, and that the distance between their centers, OP1OP2, is less than the sum of their radii, r1 + r2. Thus, the two circles touch each other internally at point P.
How can you demonstrate how two circles internally contact one another?You must calculate each circle's radius and centre in order to accomplish this. The circles will externally touch if the total of the radii and the space between the centres are identical. The circles will internally touch if the variations in radii and the separation between their centres are equal.
Let C1 and C2 stand for the two circles, with O1 and O2 serving as their respective centres. Let r1 and r2 represent the radius of C1 and C2, respectively.
Let's say that point P is where the two circles converge. The Pythagorean Theorem thus gives us:
OP1² = r1²
OP2² = r2²
OP1² + OP2² = (r1 + r2)²
Simplifying the third equation, we get:
OP1² + OP2² = r1² + 2r1r2 + r2²
The left half of this equation can be rewritten as (OP1 + OP2)2 - 2OP1OP2. When we simplify the equation above and substitute this, we get:
(OP1 + OP2)² = (r1 + r2)² + 2OP1OP2
Since OP1 and OP2 are both positive, we have:
(OP1 + OP2)²> (r1 + r2)²
Therefore, we must have:
OP1OP2 < r1 + r2
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An area of land measures 735 metres by 756 metres. It is to be divided up into
square plots of equal size.
(a) What is the area of the largest squares that will fit on it?
(b) How many squares will fit on it?
Answer:
See below!
Step-by-step explanation:
Given:Length = 735 meters
Width = 756 meters
Finding the area:Area = length × width
Area = 735 × 756
Area = 555660 m²
Part a)To find the area of largest square, we first need to find the highest common factor of 735 and 756.
HCF of 735 and 756:
= 21
This means the length of largest square will be 21 m.
Now,
Area of largest square:= length × length
= 21 × 21
= 441 m²Part b)No. of squares = Total area / Area of largest square
No. of squares = 555660 / 441
No. of squares = 1260 squares[tex]\rule[225]{225}{2}[/tex]
Which phrase is represented by the expression 5x(36+9)
A. The product of 36 and 5, increased by 9
B. The product of 36 and 9, multiplied by 5
C. The sum of 36 and 9, multiplied by 5
D. The sum of 36 and 5, increased by 9
The diameter of a child's bicycle wheel is 12 inches. Approximately how many revolutions of the wheel will it take to travel 1,200 meters? Use 3.14 for π and round to the nearest whole number. (1 meter ≈ 39.3701 inches)
Answer:
First, we need to convert 1,200 meters to inches:
1,200 meters * 39.3701 inches/meter = 47,244.12 inches
Next, we need to find the circumference of the wheel:
Circumference = π * Diameter
Circumference = 3.14 * 12 inches
Circumference = 37.68 inches
To find the number of revolutions, we can divide the total distance traveled (47,244.12 inches) by the distance traveled per revolution (37.68 inches):
47,244.12 inches ÷ 37.68 inches/revolution ≈ 1,254 revolutions
Rounding to the nearest whole number, it will take approximately 1,254 revolutions of the wheel to travel 1,200 meters on a child's bicycle.
Is -4/3 perpendicular to 3/4
Answer:
no its not
Step-by-step explanation:
Using the slope-intercept form, the slope is Undefined. The slope of a perpendicular line to a vertical line is zero.
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Express the angle in terms of degrees, minutes, and seconds, to the nearest second.
350.5527°
Answer:
350° 33' 10".
Step-by-step explanation:
To convert the decimal degree 350.5527° to degrees, minutes, and seconds, we can use the following steps:
The whole number part of the decimal degree is the degree. So, the degree is 350.Multiply the decimal part by 60 to get the minutes.0.5527 x 60 = 33.162The whole number part of the minutes is the minutes. So, the minutes are 33.Multiply the decimal part of the minutes by 60 to get the seconds.0.162 x 60 = 9.72Round the seconds to the nearest second. The nearest second is 10.Therefore, 350.5527° is equivalent to 350° 33' 10".
Compare the values for the following, which is greater: sin 100° or sin 250°? Use the sin wave to approximate
each value and label it on the graph.
The value "Sin 100°" is greater than "sin 250°", that is, sin 100° > sin 250°
Which is greater, sin 100° or sin 250°?To compare the values of sin 100° and sin 250°, we need to understand the behavior of the sine function. The sine function oscillates between -1 and 1 over a period of 360°, with its maximum value of 1 at 90° and its minimum value of -1 at 270°.
Using the sine wave, we can see that sin 100° is located in the second quadrant, where the sine values are positive, while sin 250° is located in the third quadrant, where the sine values are negative. Therefore, sin 100° is greater than sin 250°, because sin 100° has a positive value closer to the maximum value of 1, while sin 250° has a negative value closer to the minimum value of -1.
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what is the area in square centimeters, of the trapezoid below?
The area in square centimeters, of the trapezoid below is equal to 84.4 cm².
How to calculate the area of a trapezoid?In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):
Area of trapezoid, A = ½ × (a + b) × h
Where:
a and b represent the base areas of a trapezoid.
h represent the height of a trapezoid.
By substituting the given side lengths into the formula for the area of a trapezoid, we have the following:
Area of trapezoid, A = ½ × (7.9 + 13.2) × 8
Area of trapezoid, A = 84.4 cm².
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Compare the -intercepts and the rates of change of the following items.
A.The y-intercepts are the same, but the rates of change are different.
B.The items have the same y-intercept and the same rate of change.
C.The items have different y-intercepts and different rates of change.
D.The rates of change are the same, but the y-intercepts are different.
Answer:
C. The items have different y-intercepts and different rates of change
Step-by-step explanation:
Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.
Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.
Thus, we know that the rates of change are different and the y-intercepts are different for both functions.
The measure of DOT and TOU
The measure of ∠DOT is equal to 58°
The measure of ∠TOU is equal to 32°.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this mathematical equation:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
(7x + 2) + 4x = 90.
11x + 2 = 90
11x = 90 - 2
x = 88/11
x = 8.
For the measure of ∠DOT, we have;
∠DOT = (7x + 2)
∠DOT = 7(8) + 2
∠DOT = 58°
For the measure of ∠TOU, we have;
∠TOU = 4x
∠TOU = 4(8)
∠DOT = 32°.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
what is 12 plus 12 and take away 67 and then add 24
Answer:
-19
Step-by-step explanation:
First you need to add all of the positive and negative numbers together, which would look like (12+12+24) + (-67) OR 48 + -67. Now add -67 to 48.
-67 + 48 is -19. Therefore the answer is -19.
IM SO SORRY IF THIS DID NOT MAKE SENSE!
Answer:12+12=24
24-67=-43
-43+24=-19
Step-by-step explanation:
Find the surface area for the figure ( on photo )
The surface area of the square pyramid given above would be = 400ft²
How to calculate the surface area of the given shape?The diagram above is a typical example of the square based pyramid which has four triangles connected to a vertex.
To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs
where b = base length= 10ft
s = slant height= 15ft
Surface area = 100+2(10×15)
= 100+300
= 400ft²
Therefore the surface area of the square based pyramid given above would be = 400ft².
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An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation
When will the height be 230 feet?
seconds
When will the object reach the ground?
seconds
Answer:
Step-by-step explanation:
The equation for the height h of the object after t seconds is given by:
h = -16t^2 + 145t + 2
To find when the height will be 230 feet, we can set h = 230 and solve for t:
230 = -16t^2 + 145t + 2
We can simplify this equation by moving all the terms to one side:
16t^2 - 145t + 228 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 16, b = -145, and c = 228. Plugging in these values, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)
t = (145 ± sqrt(21025 - 14592)) / 32
t = (145 ± sqrt(6433)) / 32
t ≈ 0.56 seconds or t ≈ 9.17 seconds
Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.
To find when the object will reach the ground, we can set h = 0 and solve for t:
0 = -16t^2 + 145t + 2
Again, we can simplify this equation by moving all the terms to one side:
16t^2 - 145t - 2 = 0
Using the quadratic formula again, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)
t = (145 ± sqrt(21249)) / 32
t ≈ 9.51 seconds or t ≈ 0.15 seconds
Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.
~~~Harsha~~~
IREADYYYY...............................................
This is the equation that represents the situation: 3q + 7 = 40.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). An equation states that two expressions have the same value, and it provides a way to find the unknown values of variables by manipulating the expression using algebraic operations. Equations are used in a variety of fields, including physics, chemistry, engineering, economics, and many others, to model relationships and solve problems.
Here,
Let's call the length of the fourth side "x".
Since the three sides of the quadrilateral are the same length, we know that they are each equal to "q".
The perimeter of a quadrilateral is the sum of all its sides, so we can write:
q + q + q + x = 40
Simplifying, we get:
3q + x = 40
We also know that the length of the fourth side is 7 inches, so we can substitute that in for "x":
3q + 7 = 40
This is the equation that represents the situation.
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The length of a rectangle is 4 meters less than 2 inches times width. The perimeter is 34 meters. Find the width
Answer:
7
Let's call the width = x
width : x
so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7
3x = 21
x = 7
so x is 7
If z is a standard normal variable, find P(z>.97)
Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.
Standard normal distribution table explained.
A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.
The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.
For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.
Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.
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For the following sequence: 6,15,24,33,.....
a) Write an expression for the nth term
b) Find the 10th term.
Answer:
a) The common difference between consecutive terms is 9. Thus, the nth term can be expressed as:
n(9)+(-3)
b) To find the 10th term, we substitute n=10 in the expression we just found:
10(9) + (-3) = 87
Therefore, the 10th term of the sequence is 87.
Please anwser the question i will reward brainlest.
Answer:
2((3(4) + 4(7) + 3(7)) = 2(12 + 28 + 21) = 2(61) = 122 square meters
100 Points! Algebra question, only looking for an answer to B. Photo attached. Please show as much work as possible. Thank you!
Apply the fraction rule:
[tex]\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}[/tex]
Answer:
[tex]\longrightarrow\boxed{\bold{\frac{\text{fx}}{\text{g}}}}[/tex]
if x=4,then find the size of 2x+5-3x
The size of the expresssion 2x + 5 - 3x when x = 4 is 1.
What is the size of the given expression if x equal 4?Given the expression in the question:
2x + 5 - 3x
Also, x = 4
The expression 2x + 5 -3x is an algebraic expression that involves the variable x.
When we substitute x = 4 into the expression, we replace every occurrence of x with 4.
Hence
2x + 5 -3x
Replace x with 4
2(4) + 5 - 3(4)
8 + 5 - 12
Add 8 and 5
13 - 12
Subtract 12 from 13
1
Therefore, when x=4, the size of 2x + 5 - 3x is 1.
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PLS HELP DUE AT 11:59PM TODAY
Math mugshot….probability
The probability of spinning a number less than 5 is P =70%
How to find the probability?To find the probability just take the quotient between the number of numbers that are smaller than 5, and the total amount in the spinner. That is because we assume that all the regions have the same individual probability of being spun.
There are 10 in total, and of these, 7 are smaller than 5, then the probability is:
P= 7/10 = 0.7
And to write as a percent, multiply it by 100%
0.67*100% = 70%
That is the probability.
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Find the value of the annuity and the interest. Round to the nearest dollar.
Periodic Deposit: $100 at the end of each year
Rate: 4% compounded annually
Time: 9 years
The value of the annuity after 9 years is approximately $1,044.56. The interest earned on the annuity after 9 years is approximately $244.56.
What is annuity?A financial contract known as an annuity offers a series of recurring payments over a predetermined length of time. A monthly, quarterly, or annual payment schedule is available when buying an annuity from an insurance provider. The payments are made until the annuitant's death or for a predetermined amount of time.
Deferred annuities and immediate annuities are the two categories under which annuities fall. Deferred annuities are a particular kind of annuity where the payments are postponed for a predetermined amount of time, typically several years. On the other hand, an instant annuity starts paying out as soon as the annuity is bought.
The value of annuity is given by the formula:
[tex]A = P * ((1 + r)^n - 1) / r[/tex]
Substituting the given values we have:
[tex]A = $100 * ((1 + 0.04)^9 - 1) / 0.04\\A = $100 * (1.04^9 - 1) / 0.04[/tex]
A ≈ $1,044.56
Hence, the value of the annuity after 9 years is approximately $1,044.56.
Now, the interest is givn as:
Interest = A - (P * n)
Substituting the values we have:
Interest = $1,044.56 - ($100 * 9)
Interest ≈ $244.56
Hence, the interest earned on the annuity after 9 years is approximately $244.56.
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Pat's Pizza made
21
2121 cheese pizzas,
14
1414 veggie pizzas,
23
2323 pepperoni pizzas, and
14
1414 sausage pizzas yesterday.
Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza?
Choose the best answer.\
Therefore , the solution of the given problem of probability comes out to be pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
What exactly is probability?Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The total number of pizzas made yesterday can be determined using the information provided as follows:
2121 cheese pizzas total.
Pizzas with vegetables: 1414
2323 pepperoni pizzas total.
1414 sausage pizzas were consumed.
Total pizzas produced were
=>2121 + 1414 + 2323 + 1414 = 7272.
Therefore, there were 2121 cheese pizzas prepared yesterday out of a total of 7272 pizzas.
The likelihood that the following pizza will be a cheese pizza is calculated as follows:
=> 2121 / 7272
The likelihood that the next pizza prepared won't be a cheese pizza is thus:
=> 1 - (2121 / 7272) = 5151 / 7272
Therefore, a conservative estimate of the likelihood that the following pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
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Express the statement as an inequality (Part 1a^2)
a. b is positive
1. b ≥ 0
2. b ≤ 0
3. b = 0
4. b > 0
5. b < 0
b. s is nonpositive
1. s ≤ 0
2. s = 0
3. s ≥ 0
4. s < 0
5. s > 0
c. w is greater than or equal to -8
1. w < -8
2. w = -8
3. w ≥ -8
4. w > -8
5. w ≤ -8
a. 4. b > 0
If b is positive, then we know it will be greater than 0.
b. 1. s ≤ 0
If s is nonpositive, this means it is negative or 0. We will use a less than or equal to symbol.
c. 3. w ≥ -8
If w is greater than or equal to -8, we will use a greater than or equal to symbol.
If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting, how much does a 6-ounce serving cost?
$15 is the cost of a 6-ounce serving cost.
What is the cost price?
The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.
Here, we have
Given: If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting.
EP = 24 lb costing $45
1/4th lost during roasting.
Remaining = 24 lb - (1/4) of 24 lb
= 24 lb - 6 lb
= 18 lb
Now, this roast should match the cost of the original EP.
Cost per lb = (cost of beef originally)/(quantity of roasted beef)
= 45/18 dollar per lb
Cost of 6-ounce serving cost = (45/18)×6 = $15.
Hence, $15 is the cost of a 6-ounce serving cost.
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A paperwight has height of 4cm and a volume of 38.4 cubic cm.
The calculated base area of the paperweight is 9.6 square cm.
Calculating the base areaTo calculate the base area of the paperweight, we can use the formula for the volume of a three-dimensional object:
Volume = Base area x Height
In this case, we know that the height of the paperweight is 4cm and the volume is 38.4 cubic cm.
So we can rearrange the formula and solve for the base area:
Base area = Volume / Height
Substituting the values we have:
Base area = 38.4 cubic cm / 4cm
Base area = 9.6 square cm
Therefore, the base area of the paperweight is 9.6 square cm.
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The function h(x) = 2|x| is a transformation of the absolute value parent function, f(x) = |x| which graph shows h(x)
The graph of the function h(x) is then added as an attachment
Selecting the graph that best shows the function h(x)From the question, we have the following parameters that can be used in our computation:
h(x) = 2|x|
Also, we have
f(x) = |x|
When the function f(x) = |x| is compressed by a factor of 2, we do the following
We multiply 2 to the function equation
So, we have
h(x) = |x| * 2
Evaluate
h(x) = 2|x|
This means that the transformed function is passes through (x, 2y) of the original function
The graph of the function h(x) is then added as an attachment
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A student randomly selects a marble from a bag with 3 red marbles , 4 blue marbles, 2 green marbles, and 5 yellow marbles. How many outcomes are in the sample space?
There are a total of 14 possible outcomes, one for each marble in the bag.
How many outcomes are in the sample space?The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is selecting a marble from the bag.
There are 14 marbles in the bag in total.
When the first marble is selected, there will be 13 marbles remaining in the bag, then 12, then 11, and so on.
Therefore, the number of outcomes in the sample space is:
3 + 4 + 2 + 5 = 14
There are 14 possible outcomes, one for each marble in the bag.
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Due tonight at 11 please help
Thus, the height of the cylinder for the given volume and radius is found to be 10 ft.
Explain about the solid cylinder:Objects in three dimensions are represented by solid shapes. Search the area! Solid shapes include any other three-dimensional object, such as a laptop, phone, ice cream cone, balls, etc.
On a three-dimensional plane, a cylinder is a solid shape. It maintains a set spacing between two circular, parallel bases that are connected by a curved surface (like a tube).
Given that:
volume of cylinder V = 502 cu. ftRadius r = 4 ftThe formula for the volume of cylinder V:
V = πr²h
Put the values:
502 = 3.14*4²*h
502 = 3.14*16*h
h = 502 / 50.2
h = 10 ft
Thus, the height of the cylinder for the given volume and radius is found to be 10 ft.
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Complete question:
Find the missing dimension of the given solid.
The figure is attached.
A business owner applies for a credit card to cover $15,000 in emergency expenses. The credit card charges 17.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?
$21,443.51
$21,495.64
$17,934.68
$17,956.46
Answer:
(b) $21,495.64
Step-by-step explanation:
You want to know the value of $15,000 after it has earned continuously compounded interest at 17.99% for 2 years.
Compound continuouslyThe value of an account earning interest at annual rate r compounded continuously is ...
A = P·e^(rt)
where P is the initial account value, and t is the number of years.
ApplicationIn this problem, we have P=15000, r=0.1799, and t=2, so the amount due will be ...
A = $15,000·e^(0.1799·2) ≈ $21,495.64 . . . choice B
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