Using the z-distribution, the estimate for how much the drug will lower a typical patient's systolic blood pressure is:
[tex]46.6 \leq \mu \leq 48[/tex]
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 80% confidence level, hence[tex]\alpha = 0.8[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.8}{2} = 0.9[/tex], so the critical value is z = 1.28.
The other parameters are given by:
[tex]\overline{x} = 47.3, \sigma = 15.9, n = 878[/tex]
Then the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 47.3 - 1.28\frac{15.9}{\sqrt{878}} = 46.6[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 47.3 + 1.28\frac{15.9}{\sqrt{878}} = 48[/tex]
Hence the interval is:
[tex]46.6 \leq \mu \leq 48[/tex]
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Determine what type of model best fits the given situation: principal p is invested at an annual interest of rate r, compounded k times a year for t years.
The most appropriate model for a given situation is exponential.
What is compound interest?The interest you earn on interest is known as compound interest.Compound interest is a use of exponential functions. A specific sum is added to the account balance each time money is invested (or lent out). Interest is the amount of money that is added to the balance. The sum will continue to accrue interest after that interest has been added during the subsequent compounding period.In the settings of investments and savings, compound interest is used. A = P(1 + RT) is the formula for simple interest. The next section contains a definition of the variables. This indicates that the account value is the sum of the initial investment amount multiplied by one and the rate multiplied by the time.The most appropriate model for a given situation is exponential.
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Of all closed rectangular boxes of volume 64 ft3, what is the smallest surface area?
The smallest surface area of cubic rectangular boxes = 96 ft²
What is surface area?An object with three dimensions is solid and has both height and depth. A sphere and a cube, for instance, have three dimensions, whereas a circle and a square do not.
A three-dimensional shape's total surface area equals the sum of its side's surface areas. The measured area of all surfaces of three-dimensional solids, such as cubes, spheres, prisms, and pyramids, is expressed in square units.
Since it is a closed rectangular box so, there will be two equal sides.
According to the given Information:Volume = 64 ft³
Volume of rectangular cube = hx²
Surface area of rectangular cube = 2x²+4hx
Equating the above equation we get, hx² = 64
h=64/x²
Put the value of h in surface area formula,
S = 2x² + 4(64/x²)*x
S = 2x² + 256/x
For the surface area to be minimum,
ds/dx = 0
4x - (256/x²) = 0
4x³ = 256
x³ = 64
x = 4 ft
Therefore, the smallest surface area
= 2(4)² + (256/4)
S = 32 + 64
= 96 ft²
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A rectangle is 5 inches long and 2x inches wide. The value of the perimeter
(in inches) is equal to the value of the area (in square inches). Find x.
Answer:
Area=length× berngth
A=5×2x
A=10x square
the length of the sides of a triangle are in the ratio 3:4:5. find the lengths of the sides of the triangle if its perimeter is 96cm
Answer:
let the angles be 3x,4x&5x
Now,
perimeter (p)=sum of all sides
or, 96=3x+4x+5x
or, 96=12x
or,96/12=x
or,8=x
or,x=8
Then,
3x=3*8
=24
4x=4*8
=32
5x=5*8
=45
A
(5x − 3)°
B
E
(7x+15)°
D
(6y + 7)°
C
Answer:
The value of x = 14 ...
The value of ∠AED = ( 7x + 15) = 7(14) + 15 = 113
The value of ∠AEB = 5x-3 = 5(14) -3 = 67
Step-by-step explanation:
=> ∠BEC = ∠AED { vertically opposite angles }
∠AED = (7x + 15)°
=> ∠AEB + ∠BEC = 180° { linear pair }
=> ( 5x-3) + ( 7x+15) = 180°
=> 5x -3 + 7x + 15 = 180°
=> 12x + 12 = 180°
=> 12( x +1 ) = 180°
=> x+1 = 180/12
=> x +1 = 15
=> x = 15-1
=> x = 14
Which number is equivalent to (1/3)^-4
A 81
B −1/81
C −1/12
D 12
The fraction (1/3)⁻⁴ is equal to 81.
Given that:
Fraction: (1/3)⁻⁴
Rewrite the expression by applying the rule that states a negative exponent is equal to the reciprocal of the positive exponent:
(1/3)⁻⁴= 1 / (1/3)⁴
Now, let's simplify (1/3)⁴:
(1/3)⁴ = (1/3) × (1/3) × (1/3) × (1/3)
(1/3)⁴ = 1/81
So, the expression becomes:
1 /(1/3)⁴ = 1 / (1/81)
Now, dividing by a fraction is equivalent to multiplying by its reciprocal:
1 / (1/81) = 1 × 81 = 81
Therefore, the fraction (1/3)⁻⁴ is equal to 81.
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What is the range of the function in the graph?
The range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.
What is the Range and Domain of a Function?All the possible set of x-values that are plotted on the horizontal axis (x-axis) are the domain of a function. In order words, they are the inputs of the function.
On the other hand, all the corresponding set of x-values that are plotted on the vertical axis (y-axis) are the range of a function. In order words, they are the outputs of the function.
In the graph given below that shows a function, s is plotted on the vertical axis (y-axis), and its values starts from 20, up to 100. The range can be said to be all values of s that are from 20 to 100.
Therefore, the range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.
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Brandi's car holds 20 gallons of gasoline. Gas is $2.50 per gallon.
Domain:
Range:
Step-by-step explanation:
20 gallons of gasoline
gas is $ 2.50 per gallons
2.50 × 20
{(2×2)(0×.5)(0)}
domain=200
range=2.5
A coach shows the following ratio table to a team. The table shows the average amount of calories burned for a certain number of minutes of running.
Practice
Minutes of running
Calories burned
4
20
8
40
?
100
Based on the table, how many minutes does a person need to run to burn 100 calories?
12
20
28
68
Based on the table, the minutes a person has to run to burn 100 calories is 20 minutes
How many minutes does a person have to run?Ratio shows the equivalent relationship that exists between two or more numbers. A ratio table can be described as table that shows equivalent relationship between two numbers.
The first step is to determine the ratio between the minutes run and the calories burned. To do this, divide any of the minutes run on the table by the corresponding calories burned.
Ratio = minutes run / calories burned
8 / 40 = 1/5
Now, multiply this ratio by 100
1/5 x 100 = 20 minutes
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The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of
the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches
Answer:
15
Step-by-step explanation:
12 / 2 = 6
5 / 2 = 2.5
6 x 2.5 = 15
15 inches²
The cosine law is writen as question, and 2 more Questions down below. Please solve.
When to use the law of cosine is explained below.
Using the labelled triangle, we have: sin D/d = sin E/e = sin F/f.
Using the sine law, the measure of angle M is: 74.9°.
What is the Cosine Law?The cosine law is given as, c = a² + b² - 2ab(cos C). It is used to solve a triangle with missing angle or side.
What are the Two Instances When the Cosine Law is Applied?When we are given two sides and an angle between the two sides, and we need to find the third side.
When we are given the all three sides of a triangle and we need to find the angles of the triangle.
What is the Law of Sines?Using the labelled triangle DEF in the diagram below, the law of sines is:
sin D/d = sin E/e = sin F/f.
How to Find Angle M using the Law of Sines?m∠N = 56°
n = 8.5 cm
m = 9.9 cm
Plug in the values into sin N/n = sin M/m:
sin 56/8.5 = sin M/9.9
sin M = (sin 56 × 9.9)/8.5
sin M = 0.9656
M = sin^(-1)(0.9656)
M = 74.9°
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Systems requests do not deal with factors involved in improving service.
a. true
b. false
Kaitlin, Joe, and Miguel have a total 96 of in their wallets. Kaitlin has 6 less than Joe. Miguel has 4 times what Joe has. How much does each have?
Answer:
15, 11, 60
Step-by-step explanation:
Let Joe's amount be x
x + x - 6 + 4x = 96
6x - 6 = 96
6x = 90
x = 15
Joe has 15
Kaitlin has 11
Miguel has 60
The pair of triangles below have
two corresponding parts marked
as congruent. What additional
information is needed for a AAS
congruence correspondence?
Answer:
option c
Step-by-step explanation:
option c is a correct answer
Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table. A 2-column table with 4 rows is shown. The first column is labeled Blood Type with entries O, A, B, AB. The second column is labeled Number of People with entries 22, 20, 6, 2. Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
16. On your own paper, graph the following system of equations. Describe the graphs (perhaps give a few points on each line) and give the solution to the system of equations.
-2x - 5y = 20
y=4/5x+2
Answer:
(-5, 2)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-2x-5y=20\\y=\dfrac{4}{5}x+2\end{cases}[/tex]
Both equations are linear equations.
Equation 1Rearrange Equation 1 to make y the subject:
[tex]\implies -2x-5y=20[/tex]
[tex]\implies -5y=2x+20[/tex]
[tex]\implies y=-\dfrac{2}{5}x-4[/tex]
Therefore, the graph of this equation is a straight line with a negative slope and a y-intercept of (0, -4).
Find two points on the line by substituting two values of x into the equation:
[tex]x = 0\implies y=-\dfrac{2}{5}(0)-4=-4 \implies (0,-4)[/tex]
[tex]x = 5 \implies y=-\dfrac{2}{5}(5)-4=-6 \implies (5,-6)[/tex]
Plot the found points and draw a straight line through them.
Equation 2The graph of this equation is a straight line with a positive slope and a y-intercept of (0, 2).
Find two points on the line by substituting two values of x into the equation:
[tex]x = 0 \implies y=\dfrac{4}{5}(0)+2=2 \implies (0,2)[/tex]
[tex]x = 5 \implies y=\dfrac{4}{5}(5)+2=6 \implies (5,6)[/tex]
Plot the found points and draw a straight line through them.
SolutionThe solution(s) to a system of equations is the point(s) of intersection.
From inspection of the graph, the point of intersection is (-5, -2).
To verify the solution, substitute the second equation into the first and solve for x:
[tex]\implies \dfrac{4}{5}x+2=-\dfrac{2}{5}x-4[/tex]
[tex]\implies \dfrac{6}{5}x=-6[/tex]
[tex]\implies 6x=-30[/tex]
[tex]\implies x=-5[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\implies \dfrac{4}{5}(-5)+2=-2[/tex]
Hence verifying that (-5, -2) is the solution to the given system of equations.
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First simplify first one
-2x-5y=205y=-2x-20y=-2/5x-4Another one is
y=4/5x+2On first line
at x=0
y=-4At x=5
y=-2-4=-6On second line
At x=0
y=2At x=5
y=20+2=22Graph attached
Solution is (-5,-2)
Solve:
4(2 + a) = 24
A =
Answer:
a=4Step-by-step explanation:
Simplify both sides of the equation:
4 (2 + a) = 24
( 4 )( 2 ) + ( 4 )( a ) = 24 (Distribute)
8 + 4a = 24
4a + 8 = 24
subtract 8 from both sides:
4a + 8 − 8 = 24 − 8
4a = 16
Divide both sides by 4:
4 a/4 = 16/4
a = 4
Multiple bracket out first:
4 x 2 =8
4 x a = 4a
8 +4a = 24
-8
4a. = 16
÷4
a = 4
Hope this helps!
Kent has two similar cylindrical pipes, pipe a and pipe b. the radius of pipe a is 6 cm, and the radius of pipe b is 2 cm. what is the ratio of the volume of pipe a to the volume of pipe b?
The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
What is cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
Given that,
Radius of pipe a is 6 cm, and the radius of pipe b is 2 cm.
We know that the volume of cylinder is :- [tex]\pi r^{2}h[/tex]
where r is radius and h is height of the cylinder.
If two figures are similar then ratio of volume is equal to the cube of any dimension.
The ratio of the volume of Pipe a to the volume of Pipe b :-
[tex]\frac{V(a)}{V(b)}=\frac{6^{3} }{2^{3} }[/tex]
= [tex]\frac{27}{1}[/tex]
Hence, The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
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during the drive from the church to the graveyard , you cover 16,4 km in 1,5 hours . calculate your average speed
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Avg. speed = 11 km/h[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Average speed (v) :
[tex]\qquad❖ \: \sf \:v = \cfrac{total \: \: distance \: \: covered}{total \: \: time \: \: taken} [/tex]
[tex]\qquad❖ \: \sf \:v = \dfrac{16.4}{1.5} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \:v = 11 \: \: kmph[/tex]
Which characteristic is necessary to create a table that compares two functions?
The characteristic that is necessary to create a table that compares two functions is D. Choose the same values for each functions .
What is the usefulness of table?The Mathematical tables can be regarded as the lists of numbers which is used in showing the results of a calculation and these can have varying arguments.
It should be noted that when necessary to creating a table that compares two functions it is important to Choose the same values for each functions .
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Find the ordered pair (s, t) that satisfies the system.
Answer:
s is antecedent t is consepuent
13. In A ABC, if m
BF is an angle bisector, find
m
If in the triangle ABC , BF is an angle bisector and ∠ABF=41° then angle m∠BCE=8°.
Given that m∠ABF=41° and BF is an angle bisector.
We are required to find the angle m∠BCE if BF is an angle bisector.
Angle bisector basically divides an angle into two parts.
If BF is an angle bisector then ∠ABF=∠FBC by assuming that the angle is divided into two parts.
In this way ∠ABC=2*∠ABF
∠ABC=2*41
=82°
In ΔECB we got that ∠CEB=90° and ∠ABC=82° and we have to find ∠BCE.
∠BCE+∠CEB+EBC=180 (Sum of all the angles in a triangle is 180°)
∠BCE+90+82=180
∠BCE=180-172
∠BCE=8°
Hence if BF is an angle bisector then angle m∠BCE=8°.
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What is the equilibrium expression for the reaction below?
N₂(g) +
3H₂(g)2NH₂(g)
OA.
B.
OC.
OD.
3 [N₂] [H₂]
2 [NH]
[NH₂7²2
[N₂][H₂]
[NH₂]
[N₂] [H₂]
[N₂] + 3 [H₂]
2[NH₂]
The equilibrium expression is written as [NH3]^2/[N2] [H2]^3.
What is equilibrium constant?A reaction involves the conversion of reactants to products. Now we know that the number that shows us the extent to which we can convert the reactants to products is given by the equilibrium constant. If the equilibrium constant is large and positive, then the reaction tends towards the conversion of reactants to products. on the other hand, when the reaction has a small equilibrium constant, then the reaction tends towards the reactants.
Thus, the magnitude of the equilibrium constant tells us how easily reactants are converted into products and this is necessary when we are trying to predict the direction in which a reaction will go or make calculations.
Given a reaction; N₂(g) + 3H₂(g) ----> 2NH3(g) we can now write the expression for the equilibrium of the reaction as;
K = [NH3]^2/[N2] [H2]^3
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A honeybee leaves its hive and travels 100 m due west, 200 m due south, and then returns to a position 5 m north of its hive. what is its total displacement?
The total displacement of the honeybee as it travels west, south and north is 219.2 m.
Total displacement of the honeybeeThe total displacement of the honeybee is calculated as follows;
total horizontal displacement, x = 100 m due west
total vertical displacement, y = 200 m - 5 m = 195 m
total displacement, d = √x² + y²
d = √(100² + 195²)
d = 219.2 m
Thus, the total displacement of the honeybee as it travels west, south and north is 219.2 m.
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If the circumference
of a circle is
62.8 feet, what is the radius of the
circle?
Use 3.14 for I.
Hint: C = 2Tr
radius-12] foot
Please explain how you got the answer for future problems
Answer:
Hope you like my answer
Answer:
radius = 10 feet
Step-by-step explanation:
C represents the circumference.
C = 2πr ,where r is the radius.
We are given C = 62.8 ft
Equating the two expressions of C :
2πr = 62.8
Then
2 × 3.14 × r = 62.8
Then
6.28 × r = 62.8
Then
[tex]r = \frac{62.8}{6.28} = 10[/tex]
Here are the steps Tyler took to solve the equation.
Please answer these two questions! Thank youuu
Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. Thus the steps taken by Tyler are correct if x = 22.
ii. Tyler made no mistake.
Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. The value of the alphabet in the expression would be determined by applying mathematical operations appropriately.
To solve the question given to Tyler, we have:
[tex]\sqrt{x + 3}[/tex] = -5
square both sides of the equation to have;
(x + 3) = [tex](-5)^{2}[/tex]
x + 3 = 25
collect like terms to get;
x = 25 - 3
= 22
x = 22
1. Thus the equation is true if x = 22.
2. Tyler did not make any mistake in solving for x.
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The exterior surface of a farm silo needs to be painted. if one gallon of paint covers 224 square feet, what is the minimum number of gallons needed to paint the silo? keep in mind that the bottom of the silo is not painted. use π = 3.14
The gallons needed to paint the silo is 10.
How many gallons is needed to paint the silo?A cylinder is a three-dimensional object. It is a prism with a circular base. The total surface area of cylinder can be determined by adding the area of all its faces.
Total surface area of the cylinder excluding its base = 2πrh +πr²
Where:
r = radius h = heightTSA = (2 x 3.14 x 10 x 30) + (3.14 x 10²)
314 + 1884 = 2198 ft²
Number of gallons needed = 2198 / 224 = 9.81 = 10 gallons
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If 2 = x3, then x equals
A 05
B 01
C | 1
D 5
Answer:
D.
Step-by-step explanation:
if an average orange weighs 75 g, how many oranges would weigh 4.5 kg?
Answer: 60 oranges
Step-by-step explanation:
Given information
Weight = 75 g / orange
Total = 4.5 kg
Given formula
Total = Number of oranges × Average weight
Convert Kilogram unit to Gram
1 kg = 1000 g
4.5 kg = 4.5 × 1000 = 4500 g
Substitute values into the given formula
Total = Number of oranges × Average weight
Number of oranges = Total / Average weight
Number of oranges = 4500 / 75
Simplify by division
[tex]\Large\boxed{Number~of~oranges~=~60}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
60 oranges
Step-by-step explanation:
Let the unknown number of oranges be x.Given that,The average weight of an orange ⇒ 75g
Total weight of oranges ⇒ 4.5 kg
Therefore,Number of oranges Weight ( in grams)
1 75 g
x (4.5 × 1000) g
To find the number of oranges we can make an expression like this.1 ⇒ 75
x ⇒ 4500
Use cross multiplication and find the value of x.
75x = 4500 × 1
75x = 4500
Divide both sides by 75.
x = 60
Therefore, 60 oranges would weight 4.5kgHello, I need help with this. Giving brainiliest
9^(a) = (sqrt(3))^(a +2)
Answer:
2/3
Step-by-step explanation:
Let's solve your equation step-by-step.
9a=(√3)a+2
9a=1.732051a+2
Solve Exponent.
9a=1.732051a+2
log(9a)=log(1.732051a+2)(Take log of both sides)
a*(log(9))=(a+2)*(log(1.732051))
a=(log(1.732051)/log(9))*(a+2)
a=0.25*(a+2)
a=0.25a+0.5(Simplify both sides of the equation)
a−0.25a=0.25a+0.5−0.25a(Subtract 0.25a from both sides)
0.75a=0.5
0.75a/0.75=0.5/0.75
(Divide both sides by 0.75)
a=0.666667
a=2/3
0.666667=2/3
Hope this helps :)
Answer:
2/3
Step-by-step explanation:
9^a = sqrt(3)^a * sqrt(3)^2
9^a = 3^((a/2)+1)
3^(2a) = 3^((a/2)+1)
2a = (a/2)+1
1.5a=1
a=1/(3/2) = 2/3