A certain dataset of systolic blood pressure measurements has a mean of 80 and a standard deviation of 3. Assuming the distribution is bell-shaped and we randomly select a measurement:
a) What percentage of measurements are between 71 and 89?
b) What is the probability a person's blood systolic pressure measures more than 89?
c) What is the probability a person's blood systolic pressure being at most 75?
d) We should expect 15% of patients have a blood pressure below what measurement?
e) Would it be unusual for 3 patients to have a mean blood pressure measurement of more than 84? Explain.

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

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...

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!

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

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▹ Answer

180 miles

▹ Step-by-Step Explanation

Distance = mph * hours

Distance = 45 mph * 4 hrs

Distance = 180 miles

Hope this helps!

CloutAnswers ❁

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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

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).

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

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.

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!

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]

Answer:

B

Step-by-step explanation:

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

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

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°

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).

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

Answer: 1.5 less than 15 is divided by a number d.

Step-by-step explanation:

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]

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]

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

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]

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.

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.

Answer:

18/a

Step-by-step explanation:

quotient means divide

18/a

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...

Answer:

Step-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]