The number of cycles of the periodic function is 3.75 cycles if the period of a periodic function is 8 s option (G) 3.75 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The period of a periodic function is 8 s
From the question:
8n = 30
n = 30/8
n = 3.75 cycles
Thus, the number of cycles of the periodic function is 3.75 cycles if the period of a periodic function is 8 s option (G) 3.75 is correct.
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Identify an inequality you can use to find the possible values of x.
Perimeter < 51.3 inches
14.2 in.
x in.
15.5 in.
The possible values of x < 21.6.
When two mathematical statements or two numbers are compared in an unequal way, it is known as inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Different types of linear inequalities can be represented in a number of different ways. As with multi-step linear equations, start by separating the variable from the constants when resolving multi-step linear inequalities with one variable. According to the laws of inequality, it is crucial that we remember to flip the inequality sign when multiplying or dividing with negative values while resolving multi-step linear inequalities.
so, from the question, the equation becomes,
x+15.5+14.2<51.3
x= 51.3-29.7
x= 21.6 Inches
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What value (s) of x will make [tex]x^{2}[/tex] =9 true?
Select all the equations that represent the relationship between the amount of money, A, and the number of months, m.
From the given table, the equations that represent the relationship between the amount of money, A, and the number of months, m are:
C. A - 700 = 100mE. A = 700 + 100mHow to find the relationship between the variables?First, find the slope of the line:
= (1,300 - 1,200) / (6 - 5)
= 100 / 1
= 100
The slope is 100. We can use this to find the y-intercept:
y = mx + b
1,400 = 100(7) + b
b = 1,400 - 700
b = 700
The form of the relationship between the amount of money and the number of months is:
y = mx + b
y = 100x + 700
The variants of this equation are:
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FIRST PERSON TO ANSWER BRAINLIEST!!
Quadrilateral ABCD is rotated 90 degrees CCW about the origin THEN reflected across the x - axis.
What will be coordinate of C''? (no spaces in answer, use parentheses)
=======================================================
Explanation:
CCW = counter-clockwise
The rule for a 90 degree CCW rotation is this
[tex](\text{x}, \text{y})\to(-\text{y}, \text{x})[/tex]
it only works if the center of rotation is the origin.
The x and y coordinates swap places. Then you change the sign of the first coordinate after the swap occurred.
Applying that rotation rule to point C(5, 6) gets us to C ' (-6, 5).
Then to reflect over the x axis, we flip the sign of the y coordinate. The x coordinate stays the same. The notation would be [tex](\text{x}, \text{y})\to(\text{x}, -\text{y})[/tex]
So we go from C ' (-6, 5) to C '' (-6, -5)
what is the correct set of ordered pairs
A.) Find the exact value of:
1.) 7/8 + 1/6 DIVIDED BY 2/9
2.) 8/ 0.4^3
B.) A stadium has a seating capacity of 15400 seats.
1.) Calculate the # of people in the stadium when 75% of the seats are occupied.
2.) The stadium is to be renovated with a new seating capacity of 20790 seats, After the renovation, what will be the % increase in the # of seats.
C.) a NEON Flash light flashes 5 times every 10 seconds. Show that the light flashes 43200 times in a day.
D.) Expand and Simplify (2k - 3) (k -2)
There is a 35% increase in the number of seats.
What is the exact value?Let us try to carry out each of the calculations as shown;
1) 7/8 + 1/6 ÷ 2/9
Applying BODMAS
7/8 + (1/6 * 9/2)
7/8 + 9/12 = 39/24
2) 8/ 0.4^3 = 125
3) 75/100 * 15400 = 11550 people
4) Percentage increase in the number of seats = New capacity - Old capacity/Old capacity * 100/1
= 20790 seats - 15400 seats/15400 seats * 100/1
= 35 % increase
4) If it flashes 5 times every 10 seconds
Then in 1 second it flashes 0.5 times in every second
In a day there are 86400 seconds
Thus the light flashes 86400 seconds * 0.5 times = 43200 times in a day.
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7.) The height of a triangle is twice its base. The total area is 49 ft². Find the triangle's dimensions. Be sure to define
a variable, and write an equation.
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
now we also know that
the height in that triangle is twice its baseline.
so,
height = 2×baseline
so, for the given area we have
49 = baseline × 2 × baseline / 2 = baseline²
baseline = 7 ft.
therefore,
height = 2×baseline = 2×7 = 14 ft.
and now we run into a problem. as we don't have any further information about the triangle, the lengths of the sides cannot be determined.
the reason is that the height can be placed anywhere on the baseline (from the left end point all the way over to the right end point). all these triangles created by the moving height have the same area (49 ft²), but different lengths of the legs.
the lengths of the legs are calculated via Pythagoras, because the height splits the main triangle into 2 smaller right-angled triangles.
so, if I assume e.g. an isoceles triangle (both legs are equally long), then I know that the height splits the triangle into 2 equal triangles and the baseline in half.
then I can calculate :
leg² = (baseline/2)² + height² = 3.5² + 14² =
= 12.25 + 196 = 208.25
(each) leg = 14.43086969... ft
if I assume the height is at an endpoint of the baseline then the whole triangle is by itself a right-angled triangle.
and the height is one leg and the other leg is again via Pythagoras
leg² = baseline² + height² = 7² + 14² = 49 + 196 = 245
leg = 15.65247584... ft
all the possible solutions for the leg lengths are between 14 ft (the height) and 15.65247584... ft.
if DM= 25 what is the value of r
a driver of a car took a day trip around the coastline driving at two different speeds. he drove 50 miles at a slower speed and 300 miles at a speed 20 miles per hour faster. if the time spent driving at the faster speed was thrice that spent driving at the slower speed, find the two speeds during the trip.
The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.
time is calculated using the formula
[tex]Time=\frac{Distance}{Speed}[/tex]
In the given question
driver drove 50 miles at slower speed.
Let the slower speed be x miles per hour.
So the time taken to cover 50 miles at slower speed = [tex]\frac{50}{x}[/tex] ...(i)
driver drove 300 miles at faster speed.
given speed is 20 miles per hour faster i.e. speed = (x+20) miles per hour So the time taken to cover 300 miles at (x+20) mph speed = [tex]\frac{300}{(x+20)}[/tex]....(ii)
According to the question
the time spent driving at the faster speed was thrice that spent driving at the slower speed.
From equation (i) and (ii) we get
[tex]3*(\frac{50}{x} )=\frac{300}{x+20}[/tex]
[tex]\frac{150}{x} =\frac{300}{x+20}[/tex]
Cross Multiplying we get
[tex]150(x+20)=300x\\ \\ 150x+3000=300x\\ \\ 300x-150x=3000\\ \\ 150x=3000\\ \\ x=20[/tex]
Slower speed = x = 20mph.
Faster speed = (x+20) = 20+20 = 40mph.
Therefore , The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.
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Sarah bought two hot dogs that cost $1.50
each and a large soda for $2.75. How much
did she pay all together?
Answer:
$5.75
Step-by-step explanation:
price of the two hot dogs = 1.50 × 2 = $3
Then
The total payment = 3 + 2.75 = $5.75
Simplify each expression.
(-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃
The result of simplifying each number (-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃ using the exponent rules is -3
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃
Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:
(-3)¹/₃⁺ ¹/₃ ⁺ ¹/₃
(-3)³/₃
(-3)¹
-3
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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please answer the questions listed below in the SS
The answer to the following listed algebra questions are below:
6 = a/4 + 2
substract 2 from both sides
6 - 2 = a/4
4 = a/4
cross product
4 × 4 = a
a = 16
-6 + x/4 = -5
x/4 = -5 + 6
x/4 = 1
x = 4 × 1
x = 4
9x - 7 = -7
Add 7 to both sides
9x = -7 + 7
9x = 0
x = 0/9
0 = 4 + n/5
0 - 4 = n/5
-4 = n/5
-4 × 5 = n
-20 = n
-4 = r/20 - 5
-4 + 5 = r/20
1 = r/20
1 × 20 = r
r = 20
How to solve algebraic expression-1 = (5+x) / 6
-1 × 6 = (5 + x)
-6 = 5 + x
-6 - 5 = x
x = -11
(v+9)/3 = 8
v + 9 = 8 × 3
v +9 = 24
v = 24 - 9
v = 15
2(n + 5) = -2
2n + 10 = -2
2n = -2 - 10
2n = -12
n = -12/2
n = -6
-9x + 1 = -80
-9x = -80 - 1
-9x = -81
x = -81/-9
x = 9
-6 = n/2 - 10
-6 + 10 = n/2
4 = n/2
4 × 2 = n
n = 8
-2 = 2 + v/4
-2 - 2 = v/4
-4 = v/4
-4 × 4 = v
-16 = v
144 = -12(x + 5)
144 = -12x - 60
144 + 60 = -12x
204 = -12x
x = 204 / -12
x = 17
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D = m / v solve for m
The formula for density is d = M/V,
where d is density, M is mass, and V is volume.
Density is commonly expressed in units of grams per cubic cm. For example, the density of water is 1 gram per cubic cm, and Earth's density is 5.51 grams per cubic cm.
The quantity per unit volume, unit area, or unit length: as. a : the mass of a substance per unit volume. b : the distribution of a quantity (as mass, electricity, or energy) per unit usually of space.
The density is of two types, one is absolute density, and the other is relative density. Relative density is also known as specific gravity, which is the ratio of the density of a material to the density of reference material. Usually, the reference material is water.The density is of two types, one is absolute density, and the other is relative density. Relative density is also known as specific gravity, which is the ratio of the density of a material to the density of reference material. Usually, the reference material is water.The density of a liquid is a measure of how heavy it is for the amount measured. If you weigh equal amounts or volumes of two different liquids, the liquid that weighs more is more dense. If a liquid that is less dense than water is gently added to the surface of the water, it will float on the water.One way to calculate mass: Mass = volume × density. Weight is the measure of the gravitational force acting on a massto know more about mass;
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Solve each equation.
log 5 x+3=3.7
After solving the given inequality the answer is x = 0.7/5log.
When we talk about inequality, what do we really mean?Inequality is a relationship in mathematics that results from a non-equal comparison of two numbers or other mathematical expressions.On a number line, it is most commonly used to compare the sizes of two numbers.So,
Given: log5x+3 = 3.7Then,
Log·5x+3 = 3.75logx+3 = 3.7(5logx+3)+(-3) = 3.7 + (-3)x = 0.7/5logTherefore, after solving the given inequality the answer is x = 0.7/5log.
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if the work required to stretch a spring 3 ft beyond its natural length is 12 ft-lb, how much work (in ft-lb) is needed to stretch it 9 in. beyond its natural length?
The answer is 3 ft-lb.
What is the natural length of a spring?The spring's length without any attached mass is its natural length. Assuming the spring abides with Hooke's law The spring exerts a force Fs=kL if its length is altered by an amount L from its normal length, where k is a positive quantity known as the spring constant.W = 12kx2 is the amount of work required to stretch a spring x distances from its equilibrium point. Calculation information: (a) The formula is as follows: F = mg = (4 kg)(9.8 m/s2) = 39.2 N. x = 0.025 m.The spring's length at equilibrium is the length it has when no external forces are exerting any force on it. This is how spring naturally exists.
Beyond its natural length:
Work done to strech the spring to a lentgh x = 0.5 * k * x^2
Now;
12 = 0.5 * k * 9
k = 8/3 = 2.667
9 in = 1.5 ft
Work needed to stretch it 9 in. beyond its natural length = 0.5 * 2.667 * 1.5*1.5 = 3 ft-lb
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Please help me in this question
Give the answers as well as explanation
Answer:
a. 117. b. 9 c. 0. d. 22
Step-by-step explanation:
this composite function is calculated as: (f o g) (x) = f (g (x))
30 x 1/3=1 What is the property of this equation.
Answer:
[tex]x=\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]\frac{30x^1}{3}=1[/tex]
Multiply both sides by 3
[tex]\frac{3\cdot \:30x^1}{3}=1\cdot \:3[/tex]
Simplify
[tex]30x=3[/tex]
divide both sides by 30
[tex]\frac{30x}{30}=\frac{3}{30}[/tex]
Simplify
[tex]x=\frac{1}{10}[/tex]
what is the difference? -8 - 3
Answer:
-11
Step-by-step explanation:
-8-3-(8+3)-11I think it helps you
at the grocery mart, the strawberries are $2.99 for 2 lbs, and at Baldwin hills, market strawberries are $3.99 for 3 lbs round to the nearest hundredths place
The unit price of strawberries at the grocery mart is $1.5, the unit price of strawberries at the Baldwin hills is $1.30
How to solve for the unit priceIn order to get the unit price of an item, you would have to divide the cost of the item by the total quantity bought.
With this definition, at the grocery mart
price = 2.99 dollars
quantity bought = 2
unit price = 2.99 / 2
= 1.5 dollars
At the Baldwin hills
price = 3.99 dollars
quantity bought = 3
unit price = 3.99 / 3
= $1.30
Hence the unit prices at the two markets are $1.5 and $1.30
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Complete questionAt Grocery Mart,strawberries cost $2.99 for 2lb., and at Baldwin Hills Market strawberries are $3.99 for 3 lb.What is the unit price of strawberries at each grocery store? If necessary , round to the nearest penny.
Need help now pleaseeeeeeeee
What is the probability that a boy selected at random is a Junior?
P( Answer
J | B
)= Answer
Please begging of some help to finish this due today
What is the probability of randomly choosing a student who is a Junior and a boy?
P(J Answer
∩
B)= Answer
The probability that a boy selected at random is a Junior is 0.23 and the probability of randomly choosing a student who is a Junior and a boy is 0.14
What is probability?The probability of an event is the chance or the likelihood that the event would occur.
Note that the chance or the likelihood is represented as a numerical value
How to determine the probability that a boy selected at random is a Junior?The table that completes the question is added as an attachment
From the table, we have the following values
n(Boys and Junior) = 65
n(Boys) = 285
So, the probability that a boy selected at random is a Junior is
P = n(Boys and Junior)/n(Boys)
This gives
P = 65/285
Evaluate
P = 0.23
How to determine the probability of randomly choosing a student who is a Junior and a boy?From the table, we have the following values
n(Boys and Junior) = 65
Total = 465
So, the probability of randomly choosing a student who is a Junior and a boy is
P = n(Boys and Junior)/Total
This gives
P = 65/465
Evaluate
P = 0.14
Hence, the probability of randomly choosing a student who is a Junior and a boy is 0.14
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Given that 221x=25base10 find that base x
The required value of base x is -4, 3.
What is quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is
ax^2 + bx + c = 0,
where a and b are the coefficients, x is the variable, and c is the constant term.
Now it is given that,
221x = 25base10
Converting them into quadratic equation we get,
2x^2 + 2x + 1x^0 = 2*10^1 + 5*10^0
Solving we get,
2x^2 + 2x + 1*1 = 2*10 + 5*1
Multiplying we get,
2x^2 + 2x + 1 = 20 + 5
Adding we get,
2x^2 + 2x + 1 = 25
Subtracting 25 both the side we get,
2x^2 + 2x + 1 - 25 = 25 - 25
Solving we get,
2x^2 + 2x - 24 = 0
Dividing whole equation by 2 we get,
x^2 + x - 12 = 0
factorizing we get,
x^2 + (4 - 3)x - 12 = 0
Expanding the bracket we get,
x^2 + 4x - 3x - 12 = 0
Taking common we get,
x(x + 4) - 3(x + 4) = 0
Again taking common we get,
(x + 4)(x - 3) = 0
Thus the value of x are,
x = -4
and x = 3
this is the required value of base x.
Thus, the required value of base x is -4, 3.
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Hi! i have this question thats on my homework, and its due tomorrow. im no sure if its correct, can you double check for me? if you earn a manager point every 30 minutes, how many minutes would you need to work for 50 manager points?
If you earn a manager point every 30 minutes, then the number of minutes you would need to work for 50 manager points is equal to 1500.
The number of minutes needed to work for 50 manager points can be calculated using multiplication. Multiplication is one of the arithmetic parts and is thought to be the opposite of division. It represents the basic idea of the repeated addition of groups of equal sizes.
As,
one manager point = 30 minutes
50 manager points = x
Here x represents the number of minutes required to earn 50 manager points
Cross multiplying,
30 × 50 = x
x = 1500
Hence the number of minutes required to earn 50 manager points if a manager point is earned every 30 minutes is calculated to be 1500 minutes.
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14. Evaluate the expression
17 ÷ (6.5-1-21)-(-5)² - 53
4 12
Answer: 53412
Step-by-step explanation:
17
6.5−1−21
−(−5)2−
The price of gasoline is currently $3.11, this is a 14% increase from a year ago. What was the price of gas a year ago.
Answer:
2.97%
Step-by-step explanation:
Answer:
2.72807 (aprox)
Step-by-step explanation:
14% = 14/100 = 0.14
100% = 100/100 = 1
It was a increase
then 14% = 100% + 14% = 1 + 0.14 = 1.14
3.11 / 1.14 = 2.72807 (aprox)
Check:
2,72807 + (2.72807*0.14) = 2.72807 + 0.38193 = 3.11
20 plants were measured and their heights recorded in cm.
Here are the heights:
8.5
12.6
13.2
17 11.1
7.7
4.8 9.9 13.5
15.6 17.4
14
12 14.7 9.5
9.8
10
11.3
5
10
15
6.9
5
please answer :
a)
and
b)
Answer:
[tex]\begin{array}{| c | c | }{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ \bf Height, h cm& \bf Frequency\\{ \rule{3cm}0cm}&{ \rule{3cm}0cm}\\ \\ 0 < h \leqslant 5 & 2 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\5 < h \leqslant 10& 7 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ 10 < h \leqslant 15&8 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ 15 < h \leqslant 20&3 \\ { \rule{3cm}0cm}&{ \rule{3cm}0cm}\end{array}[/tex]
Step-by-step explanation:According to the topic,
We know the number of following height, h cm :-
The number of 0 < h ≤ 15 are 4.8 , 5The number of 5 < h ≤ 10 are 8.5 , 9.8 , 7.7 , 10 , 9.9 , 6.9 , 9.5The number of 10 < h ≤ 15 are 13.2 , 12.6 , 11.1 , 13.5 , 11.3 , 14 , 14.7 , 12The number of 15 < h ≤ 20 are 17, 15.4 , 17.4What is the equation of the line that passes through the point (4,-8) and has a slope of -3/4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -3/4x - 5}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = -3/4 and passes through (4, -8)}[/tex]
Find: [tex]\textsf{Determine the equation of the line that fits the criteria}[/tex]
Solution: The first thing that we need to do is plug the information that was provided into the point-slope formula, distribute, and solve for y.
Plug in the values
[tex]\textsf{y - y}_1 = \textsf{m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-8) = -3/4(x - 4)}[/tex]Distribute and simplify
[tex]\textsf{y + 8 = (-3/4 * x) + (-3/4 * -4)}[/tex][tex]\textsf{y + 8 = -3/4x + (-3 * -4)/4}[/tex][tex]\textsf{y + 8 = -3/4x + (12)/4}[/tex][tex]\textsf{y + 8 = -3/4x + 3}[/tex]Solve for y
[tex]\textsf{y + 8 - 8 = -3/4x + 3 - 8}[/tex][tex]\textsf{y = -3/4x + 3 - 8}[/tex][tex]\textsf{y = -3/4x - 5}[/tex]Therefore, the final equation of the line that passes through the point (4, -8) and has a slope of -3/4 is [tex]\textsf{y = -3/4x - 5}[/tex]
2
Select the correct answer from each drop-down menu.
Statement 1: A number is prime if and only if it only has two unique factors.
Statement 2: A number has more than two unique factors if and only if it is not prime.
Statement 2 is true v The contrapositive of a biconditional statement is
Reset
never true
always true
sometimes true
Statement 2 is true. The contrapositive of a biconditional statement is always true.
What is a conditional statement?A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
What is a biconditional statement?A biconditional statement can be defined as a statement which combines a conditional statement with its converse. This ultimately implies that, a biconditional statement is generally created when a conditional statement is combined with its converse.
In Mathematics, a biconditional statement typically has the form "P if and only if Q." Therefore, the biconditional statement, "p if q," is true whenever the two statements have the same truth value. Otherwise, the biconditional statement is false.
In this context, we can reasonably infer and logically deduce that since statement 2 is true because the contrapositive of a biconditional statement is always true.
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A rectangle has a perimeter of 64 cm. If the length is 6cm more than the width of the rectangle,
what are the dimensions of the rectangle? SHOW ALL work
Answer:
the length is 19
the width is 13
Step-by-step explanation:
well since a rectangle has two even sides the width have to be the same and the lengths have to be the same
perimeter is all the sides added together
since the length is the bigger size choose a sensible number (for example 15) and add another 15 to get the length and since it's 6cm smaller take 6 away from 15 which is 9 and add the two 9s together but 15+15+9+9 isn't 64 so you try again with a higher number until you each a total of 64
[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{Answer:-}}}[/tex]
To solve this problem, let's denote the width of the rectangle as $w$ (in cm).
According to the given information, the length of the rectangle is 6 cm more than the width, so the length can be represented as $w + 6$ (in cm).
The perimeter of a rectangle is given by the formula:
$$\text{{Perimeter}} = 2(\text{{length}} + \text{{width}})$$
Substituting the values, we have:
$64 = 2((w + 6) + w)$
Now, let's solve for $(w)$:
$64 = 2(2w + 6)$
$64 = 4w + 12$
$4w = 64 - 12$
$4w = 52$
Dividing both sides of the equation by 4, we get:
$w = \frac{{52}}{{4}}$
$w = 13$
So, the width of the rectangle is 13 cm.
Substituting the value of $w$ back into the expression for the length:
$$\text{{Length}} = w + 6 = 13 + 6 = 19$$
Therefore, the dimensions of the rectangle are 13 cm (width) and 19 cm (length).
what property of integer is this?
The expression given as -15 + 0 is a representation of the identity property of integer
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the property of integer?The expression is given as
-15 + 0
The identity property of integer states that
x + 0 = x
This means that
-15 + 0 is a representation of the identity property of integer
Hence, the expression given as -15 + 0 is a representation of the identity property of integer
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The town of Oak Manor measures 3.8 miles by 4.2 miles. Solve for the total area. (1 point)
O16 mi2
O 15.96 m²
15.96 mi
O 8 mi²