Answer:
27.5 years old
Step-by-step explanation:
We are given the formula: [tex]P=0.006A^{2} -0.02A+120[/tex] relating a patient's pressure to age.
We are also given the value for pressure (P) as 124 mmHg and need to find age (A). In order to do this, we can substitute the value 124 for P in the equation and solve the quadratic equation to obtain A:
[tex]124=0.006A^{2} -0.02A+120[/tex]
1. Set equation to 0 by subtracting 124 from both sides:
[tex]124-124=0.006A^{2} -0.02A+120-124\\= > 0.006A^{2} -0.02A-4=0[/tex]
2. Solve equation using a calculator:
It should give the solutions: [tex]A= 27.54, -24.2[/tex]
It doesn't really make sense for someone's age to be negative, therefore we can accept the positive solution as our answer.
The man whose normal blood pressure measures 124 mmHg is 27.5 years old.
Hope this helped!
One person has 1700 more than another person .Between then,they have a total of 10500. How much does each person have?
Answer:
One person will have 6100 and the other will have 4400.
Step-by-step explanation:
10500/2 = 5250
1700/2 = 850
5250+850 = 6100
10500-6100 = 4400
Check Answer:
6100+4400 = 10500
6100-4400 = 1700
1/5 + 1/3x > 1/2x - 1/4
The common denominator represent the value is X<2.7.
Get every x term on the right side and every constant term on the left to begin.
1/5+1/3 X>1/2 X-1/4
1/5+1/4+1/3 X>1/2 X
1/5+1/4>1/2 X-1/3 X
The two halves of a fraction are the numerator and the denominator. Any arithmetic operation involving two or more fractions, such as addition or subtraction, is possible if the denominators of the two fractions are the same. To this, the phrase "common denominator" relates.
When two fractions have the same denominator, we refer to them as having common denominators. Common denominators facilitate fractional operations like comparison, addition, and subtraction.
Give common denominators to the terms on each side now.
4/20+5/20>3/6 X-2/6 X
9/20>1/6 X
By multiplying both sides by 6, we may now.
27/10>X
2.7>X
Hence, the common denominator value is X<2.7.
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Find an equation of the tangent line to the curve at the given point.
y = x³ - 3x + 1, (3, 19)
Answer:
y=24x-53.
Step-by-step explanation:
1) the slope-interception view of the required tangent line is
y=slope*x+interception;
2) y'=3x²-3;
3) slope=y'(3), then slope=3*3²-3=24;
4) the required equation of tangent line has the form
y=24x+interception;
5) to calculate the interception it is needed to substitute the given coordinates (3;19) into this equation:
19=24*3+interception; ⇒ interception=-53;
6) finally, the required equation is y=24x-53.
A rectangle is 59.63 m2. If the length of the rectangle is 6.7 meters, shat is the width in meters?
Answer:
8.9
Step-by-step explanation:
When given the area of the rectangle to be 59.63m2.....AND the length to be 6.7m
To calculate the area of a rectangle = L×B
Width = Area ÷ Length
= 59.63m2 ÷ 6.7m
Width = 8.9m
Answer:
width = 8.9 meters
Step-by-step explanation:
Area of a rectangle = length * width
In this case:
Width = Area of a rectangle / length
Width = 59.63m² / 6.7m
Width = 8.9 m
Write a linear cost function for the situation. Identify all variables used.
A parking garage charges 3 dollars plus 45 cents per half-hour.
Identify all variables used. Choose the correct answer below.
Part 2 of 2
O A. C(x) represents the number of hours the parking garage was used after paying x dollars.
B. C(x) represents the number of half-hours the parking garage was used after paying x dollars.
C. C(x) represents the cost for using the parking garage for x half-hours.
OD. C(x) represents the cost for parking x cars in the parking garage.
A linear cost function for the situation is C(x) =
(Use integers or decimals for any numbers in the expression.)
Triangle PQR has vertives P(2, -4), Q(4, -5), and R(7, -2). It is translated 6 units left and 3 units up to produce Triangle P'Q'R'. Complete table.
The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.
What are the locations of the vertices of the triangle after applying rigid transformations?
In this problem we know the three vertices of a triangle on a Cartesian plane and we must determine the coordinates of its image by applying rigid transformations. According to the statement, the vertices of the image are obtained by applying a translation formula:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting point T(x, y) - Translation vectorIf we know that P(x, y) = (2, - 4), Q(x, y) = (4, - 5), R(x, y) = (7, - 2) and T(x, y) = (- 6, 3), then the coordinates of the vertices of the image are:
P'(x, y) = (2, - 4) + (- 6, 3)
P'(x, y) = (- 4, - 1)
Q'(x, y) = (4, - 5) + (- 6, 3)
Q'(x, y) = (- 2, - 2)
R'(x, y) = (7, - 2) + (- 6, 3)
R'(x, y) = (1, 1)
The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.
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Find the slope of the line if it exists.
Answer:
The slope would be [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
The governor of state A earns $54,900 more than the governor of state B. If the total of their salaries is $310,850, find the salaries of each.
Step-by-step explanation:
Let the earning of governor of state B be x then
we have,
Earning of A = 54900 + x
Earning of B = x
according to question,
Earning of A + Earning of B = 310850
54900 + x + x = 310850
2x = 255950
x = 127975
earning of A = 182875$
earning of B = 127975$
the volume of water is usually distributed with a mean of 62ml and standard deviation of 40ml. What is the probability that the volume will be greater than 90ml?
The probability of the volume of water being over 90 ml is 24.10%.
What exactly is the standard normal distribution?A symmetric probability distribution only with equal mean, mean, as well as mode values is known as a standard normal distribution.A statistical table as well as computer software is used to estimate the likelihood of a standard normal distribution.For the given question;
The mean of the sample is; μ = 62 ml.
The standard distribution is; σ = 40 ml.
The probability of the values must lie more than 90 ml.
Thus,
P(x > 90) = P[ (x - μ)/ σ ]
Substitute the values;
P(x > 90) = 1 - P[ (90 - 62)/ 40]
P(x > 90) = 1 - P[0.7]
P(x > 90) = 1 - 0.758
P(x > 90) = 0.2410
P(x > 90) = 24.10%
Therefore, the probability that the the volume of water will be greater than 90 ml is 24.10%.
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please help for brainiest !!!!
Answer:
E) Line 5
Step-by-step explanation:
Line 5 contains the first incorrect mathematical process
Process
x−5(x+1)>3x+2
−4x−5>3x+2
−7x−5>2
−7x>7
x<−1
i need help asap please
Answer:Option C J'(-3, 4), N'(1, 4), M'(1, 1), P'(-2, -1)
Step-by-step explanation:
we know that
The rule of the translation is
(x,y) -----> (x-4,y+4)
That means ----> The translation is 4 units at left and 4 units up
Find out the coordinates of the pre-image
Observing the figure
J(1,0),N(5,0),M(5,-3),P(2,-5)
Find out the coordinates of the image
Applying the rule of the translation at the coordinates of pre-image
J(1,0) -----> J'(1-4,0+4)
J(1,0) -----> J'(-3,4)
N(5,0) ---> N'(5-4,0+4)
N(5,0) ---> N'(1,4)
M(5,-3)----> M'(5-4,-3+4)
M(5,-3)----> M'(1,1)
P(2,-5) ----> P'(2-4,-5+4)
P(2,-5) ----> P'(-2,-1)
therefore
The coordinates of the image (after the transformation) are
J'(-3, 4), N'(1, 4), M'(1, 1), P'(-2, -1)
Answer:
:Option C J'(-3, 4), N'(1, 4), M'(1, 1), P'(-2, -1)
Step-by-step explanation:
My pleasure to help people
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ACDE=AOPQ?
Check all that apply.
AA
E
A. LL
B. AAS
C. SAS
D. LA
E. HL
F. ASA
Answer is ADEF
Given that, two right tringle = R + ΔHEL , R +ΔPME
Hypotenuse equal , A set of corresponding right angles are equal.{HL};
LL=LE
So ∠E(M tringle HEL)∠LM (M tringle PME)
∠H=∠P 90°
∠L=∠E ⇒AAS
HE PM or LE =EM
∠E = ∠M
EL = ME ⇒ASA
∠L = ∠E
HF = PM
∠E = ∠M ⇒SAS
EL = ME
Hence choose A.D.E.F
{Determination of congruence of right tringle }
explanation of Determination of congruence of right tringle
A plane figure bounded by three finite line segments to form a closed figure is known as a triangle. A right-angled triangle is a special case of the triangle. In a right-angled triangle, one of the interior angles measures 90°. Two right triangles are said to be congruent if they are of the same shape and size. In other words, two right triangles are said to be conger
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Solve For x
[tex] \tt \red{4x + 2 = -8}[/tex]
Thank uh ~
Answer:
The answer will be -5/2.
Step-by-step explanation:
[tex]4x + 2 = - 8 \\ subtracting \: 2 \: from \: each \: sides \: we \: get \\ 4x + 2 - 2 = - 8 - 2 \\ 4x = - 10 \\ diving \: both \: sides \: by \: 4 \: we \: get \\ \frac{4x}{4} = \frac{ - 10}{4} \\ x = \frac{ - 5 \times 2}{2 \times 2} \\ x = \frac{ - 5}{2} [/tex]
Which number line represents the solutions to lx + 4) = 2?
O
O
O
←
+++
-7 -6 -5 -4 -3 -2 -1 0
1 2
+
←
+++ ++
-7 -6 -5 -4 -3 -2 -1 0 1
┫
+
+
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
++
+
-7 -6 -5 -4 -3 -2 -1 0 1
2
3
2
+3
+
3
4
4
5
▬▬▬▬▬▬▬▬
4 5
6 7
4
+ +
6
7
5 6 7
++
5 6 7
+
eight plus the quotient of a number and 3 is 75
8 + x / 3 = 75
Minus 8 on both sides
x / 3 = 67
Multiply by 3 on both sides.
x = 201
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 430 grams. If a 32-week gestation period baby weighs 2900 grams and a 41-week gestation period baby weighs 3200 grams, find the corresponding z-scores. Which baby weighs more relative to the gestation period?
Find the corresponding z-scores. Which baby weighs relatively more? Select the correct choice below and fill in the answer boxes to complete your choice.
(Round to two decimal places as needed.)
A. The baby born in week 41 weighs relatively more since its z-score, enter your response here, is larger than the z-score of enter your response here for the baby born in week 32.
B. The baby born in week 41 weighs relatively more since its z-score, enter your response here, is smaller than the z-score of enter your response here for the baby born in week 32.
C. The baby born in week 32 weighs relatively more since its z-score, enter your response here, is larger than the z-score of enter your response here for the baby born in week 41.
D. The baby born in week 32 weighs relatively more since its z-score, enter your response here, is smaller than the z-score of enter your response here for the baby born in week 41.
Answer:
The 32 week gestation's period baby weighs 0.31 standard deviations below the mean.
The 41 week gestation's period baby weighs 0.65 standard deviations below the mean.
The 41 week gestation's period baby weighs relatively less.
Step-by-step explanation:
Normal model problems can be solved by the zscore formula.
On a normaly distributed set with mean and standard deviation , the z-score of a value X is given by:
The zscore represents how many standard deviations the value of X is above or below the mean .
Find the corresponding z-scores.
Babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 800 grams. A 32-week gestation period baby weighs 2450.
Here, we have .
So
A negative z-score indicates that the value is below the mean.
So, the 32 week gestation's period baby weighs 0.31 standard deviations below the mean.
Babies born after a gestations period of 40 weeks have a mean weight of 2900 grams and a standard deviation of 385 grams. A 41 week gestation period baby weights 2650 grams.
Here, we have
So, the 41 week gestation's period baby weighs 0.65 standard deviations below the mean.
Which baby weighs relatively less?
The 41 week gestation's period baby has a lesser z-score, so this means that he weighs relatively less.
I do not remember how to solve this
Answer:
Your answer is correct
Step-by-step explanation:
Use the rules of exponents to simplify the expression.
(q⁶)²To raise a power to another power, multiply the exponents.
q⁶ˣ²Multiply 6 by 2.
q¹²The correct option is the third.
Skandarwhich box and whiskers plot matches the data, 23, 32, 20, 13, 27, 36, 29, 38 23, 15, 30, 18, please its a test
Answer:
Option C
Step-by-step explanation:
Given the data set, 23, 32, 20, 13, 27, 36, 29, 38, 23, 15, 30, 18, to find out which box-and-whisker plot matches the data, let's work out the 5-number summary needed for constructing a box plot.
The five-number summary includes the min, Q1, median, Q3 and max value.
Let's find them.
First, order the data set from the least to the largest
13, 15, 18, 20, 23, 23, 27, 29, 30, 32, 36, 38
Min = 13
Max = 38
Median = (23 + 27) ÷ 2 = 50 ÷ 2 = 25
Q1 = (18 + 20) ÷ 2 = 38 ÷ 2 = 19
Q3 = (30 + 32) ÷ 2 = 62 ÷ 2 = 31
The box-and-whiskers plot will have the description given in option C.
Joshua purchased a game card for the arcade for a total of $20. He played three basketball hoop games for $2.25 each and two rounds of air hockey for $1.75 each. How much did he have left on the game card?
1.)$ 13.50
2.)$ 10.25
3.)$ 9.75
4.)$ 6.75
Answer:
b
Step-by-step explanation:
Joshua had $9.75 left on the game card (option 3).
Joshua's expenses on the game card can be calculated as follows:
Cost of playing three basketball hoop games = 3 games * $2.25/game
Cost of playing three basketball hoop games = $6.75
Cost of playing two rounds of air hockey = 2 rounds * $1.75/round
Cost of playing two rounds of air hockey = $3.50
Total expenses = $6.75 + $3.50
Total expenses = $10.25
Joshua originally had $20 on the game card, and he spent $10.25. To find out how much he had left, subtract his expenses from the original amount:
Amount left = $20 - $10.25
Amount left = $9.75
So, Joshua had $9.75 left on the game card.
The correct answer is 3.) $9.75.
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As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 130 milligrams of Medication A with 182 milligrams of Medication B. However this week, the doctor said to only use 140 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?
Proportionately, the number of milligrams of Medication A that should be mixed this week with 140 milligrams of Medication B is 100 milligrams.
What are proportions?Proportions are the ratios of variables to others.
Proportions show the number or value relationships of two variables.
Decimals, percentages, and fractions can represent proportions.
Data and Calculations:The mixture of Medication A and B last week:
Medication A = 130 milligrams
Medication B = 182 milligrams
The proportion of Medication A to Medication B = 0.714287
The mixture of Medication A and B this week:
Medication B = 140 milligrams
Medication A = x
x = 140 x 0.714287
x = 100 milligrams
Thus, using equivalent proportions, 140 milligrams of Medication B should be mixed with 100 milligrams of Medication A.
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The tape diagram shows that shanice spent 120 minutes researching for debate club last week?
Time that is 100% of 120 minutes is 120 minutes.
Time that is 10% of 120 minutes is 12 minutes.
Time that is 110% of 120 minutes is 132 minutes.
What are the times?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. In order to convert a number as a percentage, multiply the fraction of the number by 100. The sign used to represent percentages is %. Percentages are a measure of frequency.
Time that is 100% of 120 minutes = (100 / 100) x 120 = 120 minutes
Time that is 10% of 120 minutes = (10 / 100) x 120 = 12 minutes
Time that is 110% of 120 minutes = (110 / 100) x 120 = 132 minutes
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Answer: 100% of 120 is 120 Minutes
10% of 120 is 12 Minutes
110% of 120 is 132 Minutes
Step-by-step explanation:
There you go!
7/20 convertir de fracción a decimal
Answer: 0.35
Step-by-step explanation:
7/20 = 0.35
0.35 x 20 = 7
please help it's another urgent pt 2
Using the OR and AND operations, we have that:
a. The graph of the and operation is x > a, while the graph of the or operation is x > b.
b. The graph of the and operation is x > b, while the graph of the or operation is x > a.
c. The graphs of both operations are the same, given by x > a = x > b.
What is the result of the AND operation between two data-set?
The result of the AND operation between two data-set is the set that contains elements that belong to both sets.
What is the result of the OR operation between two data-set?
The result of the OR operation between two data-set is the set that contains elements that belong to at least one of the sets.
In item a, we have that a is to the right of b, hence:
b is plotted before a on the number line.The intersection is the values starting at a, as between b and a, there are x > b but not x > a, while for x > a, the values will belong to both sets.The or is the values starting at x > b, as they will already belong to one of the sets.Hence:
The graph of the and operation is x > a, while the graph of the or operation is x > b.
In item b, we have that a is to the left of b, hence:
a is plotted before b on the number line.The intersection is the values starting at b, as between a and b, there are x > a but not x > b, while for x > b, the values will belong to both sets.The or is the values starting at x > a, as they will already belong to one of the sets.Hence:
The graph of the and operation is x > b, while the graph of the or operation is x > a.
In item c, we have that a and b are the same point, hence, hence the graphs of both operations are the same, given by x > a = x > b.
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radius of a circle is 5 units what is the diameter
On average, Carmen can drive 33 miles on every gallon of gasoline. If she fills up her tank for $2.29 per gallon, how much will it cost her to drive 429 miles?
Answer:
$29.77
Step-by-step explanation:
First, divide 429 by 33 to find how many gallons that she's paying for, then multiply that by $2.29 to find the answer.
The cost for Carmen to drive 429 miles is $29.77.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Given that,
Distance car travels per gallon = 33 miles per gallon
Cost of gasoline per gallon = $2.29 per gallon.
33 miles can be travelled with 1 gallon of gasoline.
1 mile can be travelled with 1/33 gallon of gasoline.
429 miles can be travelled with 429/33 = 13 gallon of gasoline.
Amount of gasoline needed for 429 miles = 13 gallon.
Cost of gasoline for 1 gallon = $2.29
Cost of gasoline for 13 gallon = 13 × $2.29 = $29.77
Hence it will cost $29.77 for her to drive 429 miles.
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Ninety-six golf balls were picked up at the
driving range and placed into two buckets.
One bucket has twenty-eight more balls
than the other bucket. How many golf
balls are in each bucket?
Answer: 34 in one bucket, 62 in the other
======================================================
Work Shown:
x = number of golf balls in bucket A
y = number of golf balls in bucket B
Let's say bucket B has more golf balls. More specifically it has 28 more golf balls, so,
y = x+28
The two quantities must add to 96 golf balls total.
x+y = 96
x+x+28 = 96
2x+28 = 96
2x = 96-28
2x = 68
x = 68/2
x = 34 is the number of golf balls in bucket A
y = x+28
y = 34+28
y = 62 is the number of golf balls in bucket B
-------------
Check:
x+y = 34+62 = 96
The answer is confirmed.
Write an equation in point-slope form if (-1, 2) is a point on the line and 1/4 is the slope.
The slope or gradient of a line is a number that describes both the direction and the steepness of line. The equation in point slope form if (-1,2) is a point on the line and 1/4 is the slope is y-2=[tex]\frac{1}{4}x+\frac{1}{4}[/tex].
What is a slope?A number that identifies the direction and steepness of a line is its slope or gradient. Letter m is frequently used to represent the slope.
The ratio of "vertical change" to "horizontal change" between (any) two unique points on a line is used to compute slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
Given,
x1= -1
y1= 2
slope= 1/4
Substituting the values in the equation,
y-y1= m(x-x1)
y-2= [tex]\frac{1}{4}[/tex](x+1)
y-2= [tex]\frac{1}{4}x+\frac{1}{4}[/tex]
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The length of a rectangle is twice its width.
If the perimeter of the rectangle is 48 ft, find its length and width.
Formula we use,
→ P = 2(L + W)
Then the value of L and W is,
→ P = 2(L + W)
→ 48 = 2(2x + x)
→ 2(3x) = 48
→ x = 48/6
→ [ x = 8 ]
Then the width will be,
→ W = x = 8 ft
Hence, the width is 8 ft.
Now the length will be,
→ L = 2x = 2(8) = 16 ft
Therefore, the length is 16 ft.
PLS ANSWER. The questions is attached. Dont' put like I dont' know the answer if u don't know don't answer pls.
Answer:
x = 2.4
Step-by-step explanation:
see image for explanation.
Hope it helps
0.02,0.2,2,20,200, what is next
Answer:
0.2
Step-by-step explanation:
Answer: 2000
Step-by-step explanation:
The pattern is multiplying by 10. Therefore, 200 x 10= 2000
