Answer:
Explained below.
Step-by-step explanation:
Let X = systolic blood pressure measurements.
It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].
(a)
Compute the percentage of measurements that are between 71 and 89 as follows:
[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]
[tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of measurements that are between 71 and 89 is 99.73%.
(b)
Compute the probability that a person's blood systolic pressure measures more than 89 as follows:
[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.
(c)
Compute the probability that a person's blood systolic pressure being at most 75 as follows:
Apply continuity correction:
[tex]P(X\leq 75)=P(X<75-0.5)[/tex]
[tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]
Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.
(d)
Let x be the blood pressure required.
Then,
P (X < x) = 0.15
⇒ P (Z < z) = 0.15
⇒ z = -1.04
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]
Thus, the 15% of patients are expected to have a blood pressure below 76.9.
(e)
A z-score more than 2 or less than -2 are considered as unusual.
Compute the z score for [tex]\bar x[/tex] as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]
The z-score for the mean blood pressure measurement of 3 patients is more than 2.
Thus, it would be unusual.
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
Was is a macroeconomics
Answer:
Macroeconomics is a study that deals with the whole economy and everything pertaining to it.
Step-by-step explanation:
when we talk about Macroeconomics, we mean the whole economy. It can be related to a country's import or export, governance, how resources are accurately allocated to people in the country and the like.
Stock prices used to be quoted using eighths of a dollar. Find the total price of the transaction. 400 shares of national semi at 135 1/2
Answer:
The value is [tex]T = \$54200[/tex]
Step-by-step explanation:
From the question we are told that
The number of shares is n = 400
The rate of each share is [tex]k = 135\frac{1}{2} = 135.5[/tex]
Generally the total price is mathematically represented as
[tex]T = 400 * 135.5[/tex]
[tex]T = \$54200[/tex]
Please help with this
Answer:
B) x=80°
Step-by-step explanation:
This is a hexagon, so it has interior angles equaling 720°. (N-2)*180
So the equation would be
78+134+136+132+2x+x=720
480+3x=720
3x=720-480
3x=240
x=80°
Find the fourth roots of 16(cos 200° + i sin 200°).
Answer:
See below.
Step-by-step explanation:
To find roots of an equation, we use this formula:
[tex]z^{\frac{1}{n}}=r^{\frac{1}{n}}(cos(\frac{\theta}{n}+\frac{2k\pi}{n} )+\mathfrak{i}(sin(\frac{\theta}{n}+\frac{2k\pi}{n})),[/tex] where k = 0, 1, 2, 3... (n = root; equal to n - 1; dependent on the amount of roots needed - 0 is included).
In this case, n = 4.
Therefore, we adjust the polar equation we are given and modify it to be solved for the roots.
Part 2: Solving for root #1
To solve for root #1, make k = 0 and substitute all values into the equation. On the second step, convert the measure in degrees to the measure in radians by multiplying the degrees measurement by [tex]\frac{\pi}{180}[/tex] and simplify.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(0)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(0)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}} = 2(sin(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]
Root #1:
[tex]\large\boxed{z^\frac{1}{4}=2(cos(\frac{19\pi}{36}))+\mathfrack{i}(sin(\frac{19\pi}{38}))}[/tex]
Part 3: Solving for root #2
To solve for root #2, follow the same simplifying steps above but change k to k = 1.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(1)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(1)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{2\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{2\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{2}))\\[/tex]
Root #2:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{7\pi}{9}))+\mathfrak{i}(sin(\frac{7\pi}{9}))}[/tex]
Part 4: Solving for root #3
To solve for root #3, follow the same simplifying steps above but change k to k = 2.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(2)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(2)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{4\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{4\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\pi))+\mathfrak{i}(sin(\frac{5\pi}{18}+\pi))\\[/tex]
Root #3:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{23\pi}{18}))+\mathfrak{i}(sin(\frac{23\pi}{18}))}[/tex]
Part 4: Solving for root #4
To solve for root #4, follow the same simplifying steps above but change k to k = 3.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(3)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(3)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{6\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{6\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{3\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{3\pi}{2}))\\[/tex]
Root #4:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{16\pi}{9}))+\mathfrak{i}(sin(\frac{16\pi}{19}))}[/tex]
The fourth roots of 16(cos 200° + i(sin 200°) are listed above.
An aluminum bar 4 feet long weighs 24 pounds. What is the weight of a similar bar that is 3 feet 3 inches long? WILL MARK BL
Answer:
19.5 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.5 pounds
Answer:
19.50 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.50 pounds
What is a categorical variable
It's a variable that deals with various labels, rather than the usual type of numeric variable you may be used to.
One example of a categorical variable is color. You could have red, green, blue, yellow, and orange as the five choices for your categorical variable. Each color is a label or category.
This is an example of a qualitative variable. We don't have any numeric data attached to color. They're simply names or labels. In contrast, a quantitative variable is something like a person's height since a number is attached here (more specifically its a continuous quantitative variable).
Classify the expression: 5x + 3x^2 − 7x^3 + 2
A. Linear Expression
B. Quadratic Expression C. Cubic Expression
D. Quartic Expression
Answer:
C. Cubic expression.
Step-by-step explanation:
The highest exponent is 3 ( in the term 7x^3) so it is cubic.
Answer:
C. Cubic Expression.
Step-by-step explanation:
5x + 3x^2 - 7x^3 + 2
= 3x^2 - 7x^3 + 5x + 2
= -7x^3 + 3x^2 + 5x + 2
The highest value of exponent in the equation is 3.
For a linear expression, the highest exponent is 1.
For a quadratic expression, the highest exponent is 2.
For a cubic expression, the highest exponent is 3.
For a quartic expression, the highest exponent is 4.
So, this is C. Cubic Expression.
Hope this helps!
Joseph is 33 years old. Five years ago, He was twice as old as Ann. How old will Ann be in 5 years time?
Answer:
19 years oldStep-by-step explanation:
[tex]Joseph = 33 \:years \:old\\ \\Let \: ann's \:age be x\\\\33-5 = 2x\\\\28 = 2x\\\\Divide \:both \:sides \:of \:the \:equation \: by \:2\\\\\frac{2x}{2} = \frac{28}{2} \\\\x = 14\\\\Ann's \:present \:age \:= 14\\\\In \:5 \:years \:time ; \\\\14+5 = 19\\[/tex]
To paint his apartment, Alex but 6 gallons of paint to cover 1440 ft.². What is the ratio of square feet to gallons of paint?
Answer & Step-by-step explanation:
The ratio of square feet to gallons of paint:
[tex]1440:6[/tex]
This can also be written as:
[tex]\frac{1440}{6}[/tex]
This fraction can be simplified by dividing the numerator and denominator by 6:
[tex]\frac{1440}{6}=\frac{240}{1}[/tex]
So, the ratio of square feet to gallons of paint is:
1 gallon for every 240 ft².
:Done
Find y using the Angle Sum Theorem
Step-by-step explanation:
Hey, there!!
Look this figure, simply we find that;
In triangle ABC,
angle CBD is an exterior angle of a triangle.
and its measure is 90°
Then,
angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.
or, 90°= y + 48°
Shifting, 48° in left side,
90°-48°= y
Therefore, the value of y is 42°.
Hope it helps...
Jerry walked a dog from 6:40 a.m. to 7:30 a.m. one day. If he was paid at the rate of $6 per hour, how much did he cam that day?
how many hours are there from 10:30 on Monday to 11:30 on Tuesday
Answer:
25 hours.
Step-by-step explanation:
We are to find the number of hours from:
Monday at 10:30
to
Tuesday at 11:30
Since the question does not state whether the times are in A.M / P.M ,
There are 24 hours upto 10:30 on Tuesday.
Adding 1 hour gives 11:30
So the answer = 24 + 1 = 25 hrs
Answer:
25 hours
Step-by-step explanation:
1 day=24 hours
11.30-10.30=1 hour
----------------------------
add the total 25 hours
You calculate the correlation between height and weight for a simple random sample of 50 students from your college. Another student does the same for a simple random sample of 200 students from the college. The other student should get:_________.
A. a correlation greater than 1.
B. a higher value for the correlation.
C. about the same value for the correlation.
D. a lower value for the correlation.
E. a correlation less than-1.
Answer:
B
Step-by-step explanation:
What is the value of x to the nearest tenth?
Step-by-step explanation:
Hello!!!
Let's workout with this figure.
BC is a chord, O is the centre and OA is the perpendicular bisector.
AB = 1/2 of BC (according to circle's theorem)
so, A B = 1/2 × 25.6
Therefore, the measure of AB is 12.8.
now, let's have a small work with triangle AOB.
as it is a Right angled triangle, taking angle B as refrence angle we get,
p=x
b=12.8
h= OB = 16 (it is also a radius.)
now,
by Pythagoras relation we get,
[tex]p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
or, x = root 16^2- 12.8 ^2
by simplification, we get;
the measure of x is 9.6.
Therefore, the value of x is 9.6.
Hope it helps...
Hi i need help on this im not that smart sorry, what is the x-intercept of the graph that is shown below
Answer:
(3, 0)
Step-by-step explanation:
x-intercept is where the line touches the x-axis
It is the point on the line where y=0
Answer:
3,0
Step-by-step explanation:
the point where the line cuts the x axis is the x-intecept
Word phrase for algebraic expression 15-1.5/d
Answer: 1.5 less than 15 is divided by a number d.
Step-by-step explanation:
somebody please help
g Which of the following is equivalent to P( A|B)? a. P(A and B) b. P(B|A) c. P(A)/P(B) d. None of these choices.
Answer:
The correct option is D.
But option B is correct if P(A) = P(B).
Step-by-step explanation:
P(A|B) is read as "The probability of A given B".
It is different from the options A, B, and C.
It is equal to option B only if the probability of A is equal to the probability of B. That is P(A|B) = P(B|A) if P(A) = P(B).
You want to construct a pool that will hold 3496 ft. of water if the pool is to be 23 feet long and 19 wide how deep will it need to be
Answer:
8 feet deep
Step-by-step explanation:
volume = length x width x depth
3496 = 23 x 19 x d
3496 = 437 x d
divide both sides by 437
d = 8
Help me please thank y’all
x= 30 degrees
Step-by-step explanation:
there's 180 degrees in a triangle. You can see 60 degrees right there. Theres a 90 degree angle right next to it. 180-150=30
Can someone help I would really appreciate
Answer:
18/a
Step-by-step explanation:
quotient means divide
18/a
Which of the following units is incommensurable with kilograms
Answer:
All units of measurement that are not based on or do not measure mass or weight and volume are incommensurable with kilograms.
Step-by-step explanation:
A measure unit is said to be incommensurable with another if it does not have the same measurement basis with the other measure unit. For example, a measure in time cannot be measured in kilograms because time is measured in hours, minutes, seconds, days, etc. But, if a measurement base can be applied to two or more measurement units, then the measurement units are commensurable with the measurement base.
evaluate the expression for -c-12=
Answer:
-10
Step-by-step explanation:
We can substitute c into the equation as -2.
[tex]-(-2) - 12[/tex]
Two negatives make a positive:
[tex]2-12[/tex]
And [tex]2 - 12 = -10[/tex].
Hope this helped!
rate = 45 mph time=4 hours distance =
━━━━━━━☆☆━━━━━━━
▹ Answer
180 miles
▹ Step-by-Step Explanation
Distance = mph * hours
Distance = 45 mph * 4 hrs
Distance = 180 miles
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Please help!
Explain how changes in the dimensions of a cube dimensions affect the volume of a cube. Be specific, explaining how much the volume will change with each increase of 1 unit on the side lengths.
Answer:
when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³
Step-by-step explanation:
Let the initial length of the sides of the cube = x unit
when the length of the cube = x ; volume of the cube = length × breadth × height = x × x × x = x³ (unit)³
when the length increased by 1 unit,
new length = (x + 1) unit
New volume = (x + 1) × (x + 1) × (x + 1)
multiplying the first two brackets
New volume = (x² + 2x + 1 ) (x + 1)
espanding the brackets
New volume = x³ + 2x² + x + x² + 2x + 1
New volume = x³ + 3x² + 3x + 1 (unit)³
Change in volume:
(New volume) - (old volume)
(x³ + 3x² + 3x + 1) - (x³)
x³ + 3x² + 3x + 1 - x³
collecting like terms:
(x³ - x³) + 3x² + 3x + 1
0 + 3x² + 3x + 1
change in volume = 3x² + 3x + 1
Therefore, when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³
simplify radical -50
Answer:
[tex]5i\sqrt{2}[/tex]
Step-by-step explanation:
If we want to convert [tex]\sqrt{-50}[/tex] into a radical simplified, we need to find two numbers that multiply to be -50 and one of them can be squared.
[tex]\sqrt{-50} = \sqrt{-25 \cdot 2}[/tex]
The square root of -25 is 5i.
So:
[tex]5i\sqrt{2}[/tex]
Hope this helped!
Answer: [tex]=5i\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{-50}=\sqrt{-1}\sqrt{50}[/tex]
[tex]\sqrt{-1}\sqrt{50}[/tex]
[tex]\sqrt{5^2\cdot \:2}[/tex]
[tex]=\sqrt{2}\sqrt{5^2}[/tex]
[tex]\sqrt{5^2}=5[/tex]
[tex]=5\sqrt{2}[/tex]
Translate and solve: 54 greater than x is greater than 216
Answer:
x >162
Step-by-step explanation:
x+54 > 216
Subtract 54 from each side
x+54-54 > 216 - 54
x >162
Answer:
[tex]\huge \boxed{{x>162}}[/tex]
Step-by-step explanation:
[tex]x+54 > 216[/tex]
[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]
[tex]x+54 -54> 216-54[/tex]
[tex]x>162[/tex]
WILLL GIVE 5 STARS BRAINIEST AND THANKS AND 20 POINTS EACH ANSWER In Minot, North Dakota, the temperature was 15 degrees Fahrenheit at 4:00 P.M. By 11:00 P.M. the temperature had fallen 17 degrees. What was the temperature at 11:00 P.M.?
Answer:
-2 degrees
Step-by-step explanation:
Our original temperature is 15. We're asked to find the temperature at 11:00 P.M., which is 17 less than 15. We can set up the equation 15 - 17 to get -2. This is your answer.
Answer:
The temperature was -2 degrees Fahrenheit
Step-by-step explanation:
The starting temperature was 15 degrees
It fell 17 degrees
15 -17 = -2
The temperature was -2 degrees Fahrenheit
What is the correct standard form of the equation of the parabola? Enter your answer below. Be sure to show each step of your work.
Answer:
Step-by-step explanation:
eq. of directrix is y=4 or y-4=0
perpendicular distance of (x,y) from directrix =distance of (x,y) from focus (-3,2)
[tex]| \frac{y-4}{1}|=\sqrt{(x+3)^2+(y-2)^2} \\squaring~both~sides\\y^2-8y+16=(x+3)^2+(y-2)2\\(x+3)^2=y^2-8y+16-(y-2)^2\\(x+3)^2=y^2-8y+16-(y^2-4y+4)\\(x+3)^2=y^2-8y+16-y^2+4y-4\\(x+3)^2=-4y+12\\(x+3)^2=-4(y-3)[/tex]
