The number of heartbeat in ten minutes is 420 beats
What are unit rates?Unit rates are the rates of a quantity to one of another quantity
How to determine the number of heartbeats?From the question, the given parameters are:
Number of heartbeats per minute = 42 beats per minute -- this represents the unit rateNumber of minutes = 10 minutesThe number of heartbeats in these ten minutes is then calculated as
Total heartbeats = Number of heartbeats per minute x Number of minutes
Substitute the known values in the above equation
So, we have
Total heartbeats = 42 x 10
Evaluate
Total heartbeats = 420
Hence, the total heartbeat is 420 beats
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Type the correct answer in the box. Use numerals instead of words.
What is the solution to this equation?
3(29) 2(n + 4) = 6n
n=
-
The final value of n is -7 for linear equation 3(n - 9) - 2(n + 4) = 6n.
3(n - 9) - 2(n + 4) = 6n
6n = 3n - 27 - 2n - 8
-6n + n - 35 = 0
-5n = 35
5n = -35
n = -7
Given equation is 3(n-9)-2(n+4)=6n.
Open the brackets for multiplication, 3n - 27 - 2n - 8 = 6n.
After shifting the variables to the left-hand side and constant to the right-hand side, 5n = -35.
As the value of the constant in the above step is negative the final constant value will be also negative, n = -7.
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Line a is perpendicular to line bLine a passes through the points (1,-3) and (9,-5)Line b passes through the point (-8,32)The equation of line b is y=___
y=4x+64
Explanation:
Two lines are perpendicular if the product of their slopes is -1.
Step 1: Find the slope of the line a
Line a passes through the points (1,-3) and (9,-5)
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-5-(-3)}{9-1} \\ =\frac{-5+3}{8} \\ =-\frac{2}{8} \\ =-\frac{1}{4} \end{gathered}[/tex]The slope of line a = -1/4
Step 2: Determine the slope of line b.
Let the slope of line b = k
Since the product of the two slopes is -1:
[tex]\begin{gathered} k\times-\frac{1}{4}=-1 \\ k=-1\times-4 \\ k=4 \end{gathered}[/tex]The slope of line b = 4
Step 3: Find the equation of line b.
Line b passes through the point (x1,y1)=(-8,32) and has a slope, m = 4.
Using the slope-point form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]Substitute the given values
[tex]\begin{gathered} y-32=4\mleft(x-\mleft(-8\mright)\mright) \\ y-32=4\mleft(x+8\mright) \\ y-32=4x+32 \\ y=4x+32+32 \\ y=4x+64 \end{gathered}[/tex]The equation of line b is y=4x+64.
Fill in the missing number.
4 groups of _
equal 24.
Solve for t:
2b+2.50t=40
The value of t after solving 2b+2.50t = 40 is t = (40-2b)/2.50.
According to the question,
We have the following expression:
2b+2.50t = 40
Now, in order to find the value of t, we will move other variables and numbers from the left hand side to the right hand side.
First, moving 2b from the left hand side to the right hand side will result in the change of the sign from plus to minus:
2.50t = 40-2b
Now, 2.50 is in multiplication on the left hand side. So, it will be in the division on the right hand side.
t = (40-2b)/2.50
Hence, the value of t after solving the given expression is t = (40-2b)/2.50.
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simplify the following expression
The value of solution of expression is,
⇒ (3⁵)
We have to given that;
The expression is,
⇒ (3³ × 3⁴) ÷ 3²
Now, We can simplify by rule of exponent as;
⇒ (3³ × 3⁴) ÷ 3²
⇒ (3³ ⁺ ⁴) ÷ 3²
⇒ (3⁷) ÷ 3²
⇒ (3⁷⁻²)
⇒ (3⁵)
Thus, The value of solution of expression is,
⇒ (3⁵)
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suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. when graphed, the function gives a line with a slope of 5.9. see the figure below. with 53 gallons of fuel in its tank, the airplane has a weight of 2212.7 pounds. what is the weight of the plane with 20 gallons of fuel in its tank?
The weight of the plane with 20 gallons of fuel in its tank 2218 pounds. using a linear function.
what is linear function?
A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one.
Let y be the weight of the airplane and x be the amount of fuel
And we know that the general form of a linear
function is
(1) And given that the slope of the line is
y = mx + c
m = 5.9
Then (1) becomes
y = 5.9x + c
And given that for x = 53 , y = 2212.7
Then from (2), we have
2212.7 = 5.9 (53) + c
⇒ 2212.7 = 312.7 + c
c = 2212.7 - 312.7
c = 1900
Thus, (2) becomes
y = 5.9x + 1900
Then for x=22, from (3) y = 118 + 2100
= w = 2218
The weight of the plane with 20 gallons in its fuel tank is 2218 pounds
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Arithmetic Sequences
CAN SOMEONE PLEASE HELP ME IM BEGGING :’(
Hellow what grade of math is this?
A family drives 4 1/2 miles in 1/10 of an hour. How many miles will they drive in 3/4 hours?
Number 1 pls help show your work
Answer:
60
Step-by-step explanation:
0.2x = 12
x=60
:]
how do i create a graph of this table? and what expression should i put.
(-5 , 0) is the point we got after slope-intercept form of equation .
What exactly does slope intercept mean?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is called as the y-intercept, and the slope refers to how sharp the line is.A line has the equation 3x + 4y + 5 = 0. Using the slope intercept form, estimate the line's slope and y-intercept.Equation from the value given table -
1) y = 3x + 15
2) y = 5x + 25
3) y = 7x + 35
4) y = 9x + 45
5) y = 10x + 50
graph attached of all equation .
(-5 , 0) is the point .
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poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. find the probability of each of the following poker hands: (a) four of a kind (four cards of equal face value and one card of a different value). (b) full house (one pair and one triple of cards with equal face value). (c) three of a kind (three equal face values plus two cards of different values). (d) two pairs (two pairs of equal face value plus one card of a different value). (e) one pair (one pair of equal face value plus three cards of different values)
(a) We have 13 possibilities that a five-card hand will contain four of a kind.
(b) We have 12 possibilities that a five-card hand will contain a full house.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.
Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)
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Type the correct answer in the box. Use numbers instead of words. An expression is shown. 36 ÷ (4 + 2) What is the value of the expression?
The result of the expression 36 ÷ (4+2) is 6
The expression is
36 ÷ (4+2)
To solve this expression, we have to apply the arithmetic operations in the given expression
An arithmetic operation is the operation specified by combining number or variable with one arithmetic operator. The basic arithmetic operations are addition, subtraction, division and multiplication.
First do the arithmetic operations in the bracket
Add 4 and 2 in the expression
36 ÷ (4+2) = 36 ÷ 6
Divide the number 36 by 6 in the expression
36 ÷ 6 = 6
Hence, the result of the expression 36 ÷ (4+2) is 6
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A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. To monitor this, they take 2 oz. Of water at 37 locations every hour, measure the ph at each of those locations, and find their average. If the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8. 5 and a standard deviation of 0. 22. If the ph level of the reservoir is ok, what is the probability that the sample average is more than 8. 42?.
A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. Then the probability that the sample is more than 8.42 is 0.0029 or 0.29%.
Using the normal distribution and the central limit theorem,
The mean is μ = 8.5
The standard deviation is σ = 0.22 .
A sample of 37 is taken, hence n = 37, s = 0.22/√37 i.e. s = 0.0362
The probability that the sample average is more than 8.40 is the p-value of Z when X = 8.4, hence:
Z = X - μ/σ
Z = 8.4 - 8.5/0.0362
Z = 2.76
Z = -2.76 has a p-value 0.0029
0.0029 = 0.29% probability that the sample average is more than 8.40.
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Which statement is true?
Hope's dad gives her seven-eighths of a chocolate bar one day and then gives her six-twelfths of a chocolate bar the next day. Hope received approximately 1 chocolate bar.
Dee has ten-twelfths of a cake and gives four-eighths to her neighbor. Dee has approximately one and one-half cakes left.
Joe ran eight-fifteenth of a mile on Thursday. He ran four-fifths of a mile on Friday. Joe ran approximately one-half mile in all.
Monica swam nine-sixteenths of a mile on Tuesday. She swam one and five-eighths of a mile on Wednesday. She swam approximately 2 miles in all.
Answer:
its {A} Hope gets some of a full chocolate bar
Step-by-step explanation:
she gets 7/8 of a chocolate bar the next day she gets 6/12 7+6=13 so she gets a full chocolate bar
Please Help me immediately. this is due at 11:59pm
Priya bought these items at the grocery store. Find each unit price.
10 apples for $3.50. How much is the cost per apple?
Answer for prompt 1 10 apples for $3.50. How much is the cost per apple?
12 eggs for $3. How much is the cost per egg?
Answer for prompt 2 12 eggs for $3. How much is the cost per egg?
3 pounds of peanuts for $7.50. How much is the cost per pound?
Answer for prompt 3 3 pounds of peanuts for $7.50. How much is the cost per pound?
4 rolls of toilet paper for $2. How much is the cost per roll?
Answer for prompt 4 4 rolls of toilet paper for $2. How much is the cost per roll?
You open up a bank account with $5000. You leave it there, and the bank informs you they will add 5% annually in interest. How much money will you have earned in interest in 7 years?
A. $1850
B.$175
C.1750
D.185
Answer:
Assuming that this is referring to simple interest, your answer is C) 1,750.
Step-by-step explanation:
[tex]5000[/tex] x [tex]0.05[/tex] = [tex]250[/tex]
[tex]250[/tex] x [tex]7[/tex] = [tex]1750[/tex]
Geometry In the figure below, and . Find the values of y and z.
The measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
The figure is given in the picture:
From the property of interior angles:
x + 85 = 180
x = 95 degrees
6z - 85 + 85 = 180
z = 180/6
z = 30 degrees
Thus, the measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.
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Translate each mathematical sentence into words
Ø⊆N
"An empty set is included in set N" is the translation of the mathematical sentence.
How to translate a mathematical sentence into wordsA set is defined as a collection of well-defined objects, numbers or things. In set theory, we use different symbols to represent statements.
To translate Ø⊆N, we need to know the meaning of the symbols we have:
Ø means empty set (A set that does not contain anything).
⊆ means subset (is included in)
N means set N
So we can translate Ø⊆N as:
An empty set is included in set N or
Therefore, the mathematical sentence Ø⊆N can be translated as "an empty set is included in set N"
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Select all the values of x that are solutions of |3x - 6| = 12
A. -18
B. -6
C. -2
D. 2
E. 6
F. 18
Amy has 4 pound of ground pork to make meatballs she uses 3/8 pound per meatball to make 9 meatballs.how many 1/8 pound meatballs can Amy make with the remaining turkey ?
Amy can make 29 meatballs from the remaining beef.
What are mathematics operations?
An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.A zero-arity operation, also known as a nullary operation, is a constant.The mixed product is an example of an arity 3 operation, also known as a ternary operation.Amy has 4 pounds of ground beef to make meatballs and he uses 3/8 pound per meatball to make 9 meatballs
We have to subtract 3/8 from 4
= 4 - 3/8
= 29/8
There are 29/8 pounds of ground beef left
Therefore the number of 1/8 pound meatball that can be produced from 29/8 pounds of ground beef can be calculated as follows;
= 29/8 ÷ 1/8
= 29
Hence Amy can make 29 meatballs
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Find a quadratic model for each set of values. (1, -2), (2, -2), (3, -4)
Answer:
f(x) = ax^2 + bx + c
I) f(1) = a + b + c = -2
II) f(2) = 4a + 2b + c = -2
III) f(3) = 9a + 3b + c = -4
II - I
IV) 3a + b = 0
III - I
V) 8a + 2b = -2
V - 2IV
2a = -2 --> a = -1
3(-1) + b = 0 --> b = 3
(-1) + (3) + c = -2 --> c = -4
f(x) = -x^2 + 3x - 4
Using the concept of a net rate introduced in Problem 2, determine a differential equation governing a population P(t) if the birth rate is proportional to the population present at time t but the death rate is proportional to the square of the population present at time t.
We may be thinking about either of these choices depending on whether we are talking about immigration or emigration.
[tex]\frac{d P}{d t}=r_g \pm r[/tex]
This is further explained below.
What is a differential equation?Generally, The rates of births and deaths will be represented accordingly by the superscripts [tex]r_b[/tex] and [tex]r_d[/tex].
The model transforms into the following when subjected to the circumstances outlined in the problem:
[tex]\frac{d P}{d t}=r_b P-r_d P^2[/tex]
In conclusion, You need to submit model 1 in order to get more information.
In the event that the proportionality assumptions about birth and death be loosened up, the model that is necessary for issue 1 would become the following:
[tex]\frac{d P}{d t}=r_g \pm r[/tex]
Depending on whether we are discussing immigration or emigration, we may be contemplating either of these options.
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what is the equation of a line perpendicular to y=2x-6 that passes through (5,4)?
Answer:
[tex]y = -\dfrac{1}{2}x + \dfrac{13}{2} \;\; \text{or}\\\\y = -0.5x + 6.5\\\\[/tex]
Step-by-step explanation:
The slope-intercept form of a straight line is
y = mx + b
where m = slope and b = y-intercept
A line perpendicular to the above line will have a slope = -1/m and an intercept b which has to be determined depending on a point the line passes through
Given
Line 1: y = 2x - 6
Slope m = 2
Line 2 perpendicular to Line 1 will have slope = -1/2 = -0.5
So the equation would be y = (-1/2)x + b
We can solve for b given the info that the line passes through (5,4)
Substitute x = 5 and y = 4 in line 2 equation:
4 = (-1/2)5 + b
4 = -5/2 + b
4 + 5/2 = b
8/2 + 5/2 = b
13/2 = b
or b = 13/2
So equation of line perpendicular to 2x -6 is
y = (-1/2)x + 13/2
or
y = -0.5x + 6.5
What is an equation of the line that passes through the point (-4,8)(−4,8) and is parallel to the line x+y=6x+y=6?
The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 is; x + y = 4.
What is the equation of the line that passes through the given point and is parallel to the given line?By expressing the given linear equation in slope-intercept form; it follows that we have;
x + y = 6
y = -x + 6
Hence, the slope of the equation by comparison with; y = mx + c is; -1.
Therefore, the slope of the required equation is same as the two lines are said to be parallel.
Therefore, the required equation from point-slope form of an equation is;
( y - 8) = -1 ( x - (-4))
y - 8 = -x - 4
x + y = -4 +8
x + y = 4.
Ultimately, the required equation is; x + y = 4.
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if q= (7 -1) and r= (-4 5) find | q+ r|
Answer: 6+1=7
Step-by-step explanation:
the unit circle has center ▼ left parenthesis 1 comma 1 right parenthesis left parenthesis negative 1 comma negative 1 right parenthesis left parenthesis 0 comma 0 right parenthesis and radius ▼ 1. negative 1. startroot 2 endroot . the equation of the unit circle is ▼ y equals mx plus b. x squared plus y squared equals 1. y equals ax squared .
x^2+ y^2-2x-2y = 0 has center (1,1) and radius sqrt 2 and the circle x^2+y^2 =1 has center (0,0) and radius 1
the unit circle has center
(1,1) , ( 0,0)
and the unit circle has radius
1 , sqrt 2
for this the equation of the circle is
x^2 + y^2 = 1
if we take center as (0,0) then radius become 1
therefore equation of circle becomes x^2 +y^2 =1
similarly if we take center ( 1,1 ) and radius sqrt 2
then (x -1 )^2 + ( y-1 )^2 =2
x^2 +y^2 -2x- 2y +2 =2
this implies x^2 +y^2 -2x -2y =0
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triangle ABC is dilated by a factor of 1/4. What will be the length of side AB after the dilation?
The length of side AB after the dilation is 2 units.
Given that, ΔABC is dilated by a factor of 1/4.
What is a scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized.
The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.
From the given figure, AB=8 units, BC=6 units and AC=10 units.
Let the x be the length of side AB after the dilation.
Now, using scale factor formula 1/4 = x ÷ 8
⇒x=2 units
Therefore, the length of side AB after the dilation is 2 units.
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Factor this trinomial x^2+8x+12
Reason:
We look for two values that
a) multiply to 12b) add to 8Using trial and error, you should find those two values are 2 and 6
2 times 6 = 122 plus 6 = 8This is how we arrive at (x+2)(x+6)
Use the FOIL rule to expand that out and you should get x^2+8x+12 to confirm the answer.
Write the conditional and converse of the statements below:
"parallel lines have the same slope."
Converse of the statements will be as If two lines are parallel, then they have equal slopes. Conditional statement will be; If two lines have same slopes, then the lines are parallel.
How do parallel lines work?Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.
Only the slopes of two lines are same then it can be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel.
Converse of the statements will be as If two lines are parallel, then they have equal slopes.
Conditional statement will be; If two lines have same slopes, then the lines are parallel.
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Which two transformations can be used to obtain the graph of G(x) = -4√x , from the graph of F(x)=√x?
Given: The base function
[tex]F(x)=\sqrt{x}[/tex]To Determine: The transformation that would give the function G(x)
[tex]G(x)=-4\sqrt{x}[/tex]Solution
Let us plot the graph of the base function and the new function as shown below
It can be observed that there exist a reflection across the x-axis, also a vertical stetch by a factor of 4
Hence, the correct answer is a vertical stretch by a factor of 4, followed by a reflection across the x-axis, OPTION A