The Answer for the given functions are:
i) f(-3) = -14.
ii) g[f(0)] = -16.
iii) f[h(2)] = 13.
iv) hᴏf(x) = 3x - 1.
v) h-1(1) = -3.
What is the functiοn nοtatiοn?Functiοn nοtatiοn is a way οf representing a functiοn using algebraic symbοls. It is a shοrthand way οf expressing a relatiοnship between twο quantities οr variables, where οne variable depends οn the οther.
i) Tο find f(-3), we substitute x = -3 in the expressiοn fοr f(x) and simplify:
f(-3) = 3(-3) - 5 = -9 - 5 = -14
Therefοre, f(-3) = -14.
ii) Tο find g[f(0)], we first evaluate f(0) and then substitute that value intο g(x):
f(0) = 3(0) - 5 = -5
g[f(0)] = g(-5) = 2(-5) - 6 = -10 - 6 = -16
Therefοre, g[f(0)] = -16.
iii) Tο find f[h(2)], we first evaluate h(2) and then substitute that value intο f(x):
h(2) = 2 + 4 = 6
f[h(2)] = f(6) = 3(6) - 5 = 18 - 5 = 13
Therefοre, f[h(2)] = 13.
iv) Tο find hᴏf(x), we substitute f(x) intο the expressiοn fοr h(x) and simplify:
hᴏf(x) = h[f(x)] = f(x) + 4 = (3x - 5) + 4 = 3x - 1
Therefοre, hᴏf(x) = 3x - 1.
v) Tο find h-1(1), we need tο sοlve fοr x in the equatiοn h(x) = 1:
h(x) = x + 4 = 1
Subtracting 4 frοm bοth sides, we get:
x = 1 - 4 = -3
Therefοre, h-1(1) = -3.
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3. There are 15 students in class 7 who need the school shirt of same size and 2 meter of
cloth is required to make a shirt.
(a) Find the total length of the cloth required to make the shirt to them.
(b) How many shirts can be made from a piece of cloth 9 meter long?
Convert the length of cloth required for a shirt in decimal.
1
If the length of a piece of cloth is 36.25 meter, how many meters of cloth is left? 1
Answer:
Step-by-step explanation:
(a) Since each student needs a shirt of the same size, and 2 meters of cloth is required to make one shirt, the total length of cloth required to make shirts for 15 students would be:
Total length of cloth = 15 x 2 = 30 meters
Therefore, 30 meters of cloth would be required to make shirts for 15 students.
(b) If 2 meters of cloth are required to make one shirt, then the number of shirts that can be made from 9 meters of cloth would be:
Number of shirts = 9 / 2 = 4.5 shirts
However, since we cannot make half a shirt, the actual number of shirts that can be made from 9 meters of cloth would be 4 shirts.
To convert the length of cloth required for a shirt into decimal form, we can simply divide the length in centimeters by 100. Therefore, 2 meters of cloth would be equivalent to 200 centimeters, which is 2.00 meters in decimal form.
(c) If the length of a piece of cloth is 36.25 meters, and we use 30 meters to make shirts for 15 students, then the remaining length of cloth would be:
Remaining length of cloth = 36.25 - 30 = 6.25 meters
Therefore, 6.25 meters of cloth would be left.
Find a number between 100 and 200 which is also equal to a square number
multiplied by a prime number.
Answer:
162, 147 etc.
Step-by-step explanation:
we have to find
[tex]N = k^2 \cdot p[/tex]
we can iterate k = 1 to 10 to check all possible solutions,
[tex]N = 9^2 \cdot 2[/tex]
[tex]N = 7^2 \cdot 3[/tex]
N = 162, 147 etc.
Hopefully this answer helped you!!
Perry's patio is 6 meters long and 53 meters wide. What is the area of his patio?
19
Find the area of the triangle.
B
14
16
units squared
Since we are given the lengths of the two legs of the triangle, 14 and 16 respectively, the area of the triangle is 152.97 square units.
What is the area of this triangle?To find the area of a triangle, we can use the formula: area = (1/2) x base x height
In this case, we are given the lengths of the two legs of the triangle, 14 and 16, so we can use the Pythagorean theorem to find the length of the base:
a^2 + b^2 = c^2
14^2 + 16^2 = c^2
196 + 256 = c^2
452 = c^2
c = √452
c ≈ 21.26
To find the height, we need to drop a perpendicular from the apex to the base, forming two right triangles. Using the Pythagorean theorem again, we have:
(1/2) x base x height = area
(1/2) x 21.26 x height = area
Let's use the right triangle with legs 14 and height h as our reference. Then we have:
h^2 + 7^2 = 16^2
h^2 + 49 = 256
h^2 = 207
h = √207
h ≈ 14.39
Therefore, the area of the triangle is:
= (1/2) x 21.26 x 14.39
= 152.9657
= 152.97².
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If lines, KI and LY, intersect at point A and m/KAY=4x+39, m/LAI=12x-9, what is m/YAI?
Answer:
0 degrees
Step-by-step explanation:
To find m/YAI, we need to first find the measure of angle KAI, which is the sum of angles KAY and LAI. Then, we can find the measure of angle YAI by subtracting the measure of angle KAI from 180 degrees.
Using the angle addition postulate, we know that:
m/KAY + m/LAI = m/KAI
Substituting the given values, we get:
4x + 39 + 12x - 9 = m/KAI
Simplifying the expression, we get:
16x + 30 = m/KAI
Now, we need to solve for x. To do this, we can use the fact that angles KAY and LAI are supplementary (add up to 180 degrees) since they form a straight line. Thus:
m/KAY + m/LAI = 180
Substituting the given values, we get:
4x + 39 + 12x - 9 = 180
Simplifying the expression, we get:
16x + 30 = 180
Subtracting 30 from both sides, we get:
16x = 150
Dividing both sides by 16, we get:
x = 9.375
Now that we know x, we can substitute it back into the equation we found earlier:
16x + 30 = m/KAI
16(9.375) + 30 = m/KAI
150 + 30 = m/KAI
m/KAI = 180
So, we know that angle KAI measures 180 degrees. To find m/YAI, we need to subtract the measure of angle KAI from 180 degrees:
m/YAI = 180 - m/KAI
m/YAI = 180 - 180
m/YAI = 0
Therefore, we can conclude that the measure of angle YAI is 0 degrees. This means that YAI is not an angle, but a line segment, and it does not have a measure in degrees.
Which function is a translation one unit right of the function
f(x) = log x?
Answer:
g(x)= log(x-1)
Step-by-step explanation:
g(x) = f(x-1)
Jump to level 1
What are m and b in the linear equation 3 + 7x + 11 + 10x = y?
m = Ex: 50 ÷
b = Ex: 50
Answer:
The given equation is 3 + 7x + 11 + 10x = y.
Simplifying the equation, we get:
y = 17x + 14
Comparing with the standard linear equation y = mx + b, we can see that:
m = 17
b = 14
Therefore, m = 17 and b = 14.
Express the trig ratios as fractions in simplest terms.
cOS K =
sin L=
cos K and sin L
Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.
Trigonometric Ratios of Particular Angles: What Are They?It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.
The Pythagorean formula can be applied to the illustration to determine the length of the third side:
c²= a²+ b²
c²= 8² + √(17)²
c²= 64 + 17
c² = 81
c = 9
We can now calculate the trigonometry ratios of angles K and L:
cos(K) = adjacent/hypotenuse = √(17)/9
sin(L) = opposite/hypotenuse = 8/9
Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:
cos(K) = adjacent/hypotenuse = √(17)/9
sin(L) = opposite/hypotenuse = 8/9
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Look at the following set of four whole numbers. 4 9 10 12 Find another set of four whole numbers so that: the range has increased by 2, • the mean remains the same, • the median has decreased by 1. ● You may use some of the numbers from the orignal set, but not exactly the same four numbers. My four numbers are
The required set of numbers 5, 9, 11, and 14 satisfies all the given conditions.
What is Set?In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.
According to question:a set of four whole numbers that satisfies the given conditions:
5, 9, 11, 14
To check that this set meets the requirements:
The range of the original set (12 - 4 = 8) increased by 2 to become 10 (14 - 4 = 10).
The mean of the original set ((4 + 9 + 10 + 12) / 4 = 8.75) remains the same in the new set ((5 + 9 + 11 + 14) / 4 = 8.75).
The median of the original set is 9.5 (the average of 9 and 10), and the median of the new set is 10 - 1 = 9.
Therefore, the set of numbers 5, 9, 11, and 14 satisfies all the given conditions.
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Help with this trig identities problems.
1) Given csc Φ = 7/3 and cot Φ = - (2√10)/(3), find sec Φ.
2) Given that sec β = 6/5 and sin β > 0, find tan β and sin β.
Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.
1. We can start by using the Pythagorean identity to find the values of sin Φ:
[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1
Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:
1/(7/3) = sin Φ
sin Φ = 3/7
Next, we can use the fact that cot Φ = cos Φ/sin Φ:
cot Φ = cos Φ/(3/7) = - (2√10)/(3)
Simplifying this expression, we get:
cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7
Finally, we can use the fact that sec Φ = 1/cos Φ:
sec Φ = 1/(- 2√10/7) = -7/(2√10)
2. We can use the fact that sec β = 1/cos β to find the value of cos β:
sec β = 6/5
cos β = 5/6
Next, we can use the Pythagorean identity to find the value of sin β:
[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1
sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6
Finally, we can use the fact that tan β = sin β/cos β:
tan β = (√11/6)/(5/6) = √11/5
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What values of y and z make
The values of y and z which makes triangle (△) QRS exactly the same (≅) as triangle (△) WVX is
y = 11z = 11How do i determine the value of y?We must note here that the sign, ≅ means exactly the same. Thus,
Line VW = Line QR
The following were obtained from the question:
Line VW = 31Line QR = y + 20Value of y =?Line VW = Line QR
31 = y + 20
Collect like terms
y = 31 - 20
y = 11
Thus, the value of y is 11
How do i determine the value of z?We can obtain the value of z as follow:
Line QS = Line WXLine QS = y + 3z + 28Line WX = 6y + z - 5Value of y = 11Value of z =?Line QS = Line WX
y + 3z + 28 = 6y + z - 5
11 + 3z + 28 = 6(11) + z - 5
11 + 3z + 28 = 66 + z - 5
3z + 39 = z + 61
Collect like terms
3z - z = 61 - 39
2z = 22
Divide both sides by 2
z = 22 / 2
z = 11
Thus, the value of z is 11
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1pt equal how many mL
Answer:
1 American pt equals approximately 568.261 mL
OR
1 British Imperial pt is approximately 473 mL
I recommend choosing the answer that better relates to where you are from.
Step-by-step explanation:
There seem to be TWO kinds of pint sizes. A US pint is 16 ounces and an Imperial pint is 20 ounces.
Solve for x. Round to the nearest tenth.
x =
(30 points)
The value of x round to the nearest 10th is 28.
One of the most significant areas of mathematics is trigonometry, which has numerous applications. The study of the relationship between the sides and angles of the right-angle triangle is the main objective of the branch of mathematics known as "trigonometry." Trigonometric identities, functions, and formulas can be used to determine the angles or sides of a right triangle that are unknown or missing. Angles can be expressed in trigonometry as either degrees or radians. The five most frequently used trigonometric angles in calculations are 0°, 30°, 45°, 60°, and 90°.
In the given right-angled triangle the angle is 41 degrees and the altitude is 32 units.
So, the trigonometry ratio is -
[tex]tan \theta=\frac{32}{x}\\\\x= 32 tan41\\\\x=28[/tex]
the value of x=28
The complete question is'
Find the value of x in a given triangle, and round to the nearest tenth,
image of the triangle is attached,
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ASAP !
[tex]2 \frac{3}{6} - \frac{1}{3} [/tex]
The mathematical expression to be evaluated is:
[tex]2 \frac{3}{6} - \frac{1}{3}[/tex]
To simplify the expression, we first convert the mixed fraction to an improper fraction:
[tex]2 \frac{3}{6} = \frac{(2 \times 6) + 3}{6} = \frac{15}{6}[/tex]
Substituting this value back into the original expression, we get:
[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{15}{6} - \frac{1}{3}[/tex]
Now we need to find a common denominator for the two fractions:
[tex]\frac{15}{6} - \frac{1}{3} = \frac{15}{6} \times \frac{2}{2} - \frac{1}{3} \times \frac{2}{2} = \frac{30}{12} - \frac{2}{6}[/tex]
We can simplify the second fraction:
[tex]\frac{30}{12} - \frac{2}{6} = \frac{30}{12} - \frac{4}{12} = \frac{26}{12}[/tex]
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
[tex]\frac{26}{12} = \frac{13}{6}[/tex]
Therefore, the simplified value of the mathematical expression is:
[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{13}{6}[/tex]
Answer:
[tex]2\frac{1}{6}[/tex]
Step-by-step explanation:
First, write the fractions as improper fractions.
[tex]\sf2\frac{3}{6} -\frac{1}{3} \\\\\sf\frac{15}{6} -\frac{1}{3}[/tex]
To, subtract the fractions make the denominators the same.
For that, multiply both sides of 1/3 by 2.
[tex]\sf\frac{15}{6} -\frac{1*2}{3*2} \\\\\sf\frac{15}{6} -\frac{2}{6}[/tex]
Subtract.
[tex]\frac{13}{6}[/tex]
Write it as a mixed number.
[tex]2\frac{1}{6}[/tex]
The equation P=7h gives the amount of pay (P) you earn for working h hours. Identify the independent and dependent variables. How my do you earn after 8 hours of work?
Earn 56 units of currency after 8 hours of work.
What is independent variable?
The independent variable is the variable that you change and control in your experiment.
The independent variable is the number of hours worked, h. The dependent variable is the amount of pay earned, P.
To find how much you earn after 8 hours of work, we can simply substitute h = 8 into the equation and evaluate:
P = 7h
P = 7(8)
P = 56
So you would earn 56 units of currency after 8 hours of work.
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EL TRIPLE DE X MENOS CINCO DIVIDIDO ENTRE EL PRODUCTO DE SEIS Y X CUAL ES LA EXPRECION EQUIVALENTE?
Answer:
Step-by-step explanation:
Answer:
= 3x - 5/(6x)
Step-by-step explanation:
El triple de x es: 3x
La expresión es:
3x - 5/(6x)
Please helpppp I need helppp please
The value of x in the rectangle is 36.
How to find the angle of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
All angles measure 90∘ in a rectangle. The sum of angles in a rectangle is 360 degrees.
Therefore, let's find the value of x in the angles.
Hence,
∠2 = x + 30
∠5 = 2x - 48
Therefore,
∠2 + ∠5 = 90°
x + 30 + 2x - 48 = 90
3x - 18 = 90
3x = 90 + 18
3x = 108
divide both sides by 3
x = 108 / 3
x = 36
Therefore,
x = 36
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ABCD is a square. P and D are points on the y-axis. A is a point on the x-axis. PAB is a straight line. The equation of the line that passes through the points A and D is y=-2x+6. Find the length of PD.
The length of the segment PD obtained using the relationship between similar right triangles is; PD = 7.5 units
What is a right triangle?A right triangle is a triangle that has an interior angle of 90° (a right angle) and the side opposite the right angle (90°) interior angle is known as the hypotenuse side, while the other two sides of the triangle are the legs of the right triangle.
The possible drawing in the question, obtained from a similar online question, created with MS Word is attached.
The equation of the line that passes through the points A and D, y = -2·x + 6, indicates;
The coordinates of the y-intercept of the line of the equation, is; (0, 6)
The y-intercept indicates that OD = 6 units
The x-intercept coordinates of the graph of the equation, can therefore be obtained as follows; 0 = -2·x + 6
2·x = 6
x = 6/2 = 3
x = 3
The x-intercept is; (0, 3)
The x-intercept indicates that OA = 3 units
The length of the side of the square, s, is therefore;
s = √(s²) = √(6² + 3²) = 3·√5
OA = The length of the x-intercept of ; y = -2·x + 6
The ∠DAO ≅ ∠OPA, and m∠DOA = m∠POA = 90°
Therefore;
∠DOA ≅ ∠POA
ΔOPA is similar to ΔOAD, by Angle-Angle similarity postulate
The ratio of corresponding sides of similar triangles indicates;
OP/OA = OA/OD
Therefore;
OP/OA = OA/OD
OP/3 = 3/6
OP = 3 × 3/6 = 1.5
PD = OP + OD (Segment addition postulate)
PD = 1.5 + 6 = 7.5
The length of segment PD is 7.5 unitsPlease find attached the possible drawing in the question, created with MS Word, obtained from a similar question posted online.
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mework
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Part 1 of 3
A group consists of five Democrats and six Republicans. Three people are selected to attend a conference
a. In how many ways can three people be selected from this group of eleven?
b. In how many ways can three Republicans be selected from the six Republicans?
c. Find the probability that the selected group will consist of all Republicans
a. The number of ways to select three people from the group of eleven is
Therefore, there is a 12.12% chance that the chosen party will be made up exclusively of Republicans.
what is probability ?The likelihood or chance of an occurrence occurring is measured by probability. The occurrence is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. Numerous disciplines, including statistics, mathematics, science, finance, and engineering, heavily rely on probability to make predictions and judgments about the chance of various events happening.
given
A. The combination formula can be used to determine how many options there are to choose three individuals from a group of eleven:
C(11, 3) = 11! / (3! (11-3)!) = 165
There are 165 different methods to choose three from this group of eleven people.
b. The combination formula gives the number of options to choose three Republicans from the group of six Republicans:
C(6, 3) = 6! / (3! (6-3)!) = 20
To choose three Republicans from this set of six Republicans, there are 20 possible options.
c. The ratio of the number of ways to choose three Republicans from the group of six Republicans to the total number of ways to choose three people from the group of eleven determines the likelihood of choosing three Republicans out of the group of eleven.
P(3 Republicans) = C(6, 3) / C(11, 3), which translates to 20 / 165 = 0.1212 or roughly 12.12%.
Therefore, there is a 12.12% chance that the chosen party will be made up exclusively of Republicans.
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5. Find the volume of the cylinder. Leave your
answer in terms of t.
8 cm.
8 cm.
The volume of the cylinder in terms of π is 128π centimetres³.
How to find the volume of a cylinder?The cylinder below has a height of 8 centimetres and a diameter of 8 centimetres. Therefore, the volume of the cylinder can be found as follows:
volume of the cylinder = πr²h
where
r = radiush = height of the cylinderTherefore,
r = 8 / 2 = 4 centimetres
h = 8 centimetres
volume of the cylinder = π × 4² × 8
volume of the cylinder = 128π centimetres³
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i need so help plez average weight of a male African elephant is 15,000 pounds. How many tons is this?
7 tons
8 tons
7 tons 1000 pounds
30,000,000 tons
Step-by-step explanation:
The average weight of a male African elephant is 15,000 pounds.
To convert pounds to tons, we divide the weight in pounds by 2,000 (the number of pounds in a ton):
15,000 pounds ÷ 2,000 pounds/ton = 7.5 tons
Therefore, the weight of a male African elephant is approximately 7.5 tons.
So the closest answer to this question is "7 tons".
Answer:
7 tons
Step-by-step explanation:
The average weight of a male African elephant is 15,000 pounds. To convert this weight into tons, we need to divide it by 2,000 (since there are 2,000 pounds in a ton).
So, 15,000 ÷ 2,000 = 7.5 tons.
Therefore, the answer is 7 tons (since there are no fractions of tons in the options given).
Which graph represents the function f(x) = −|x − 2| − 1?
A.
B.
C.
D.
"^ a popular shopping Centre waiting time for an ABC Ban ATM machine is found to be uniformly distributed between 1 and 5 minutes. what is the probability of waiting between 2 and 3 minutes to use the ATM
The probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur. For example, the probability of flipping a fair coin and getting heads is 1/2 or 0.5.
Since the waiting time for the ABC Ban ATM machine is uniformly distributed between 1 and 5 minutes, the probability density function is given by:
f(x) = 1/(5-1) = 1/4 for 1 ≤ x ≤ 5
To find the probability of waiting between 2 and 3 minutes, we need to find the area under the probability density function between 2 and 3. This is given by the definite integral of the probability density function over the interval [2, 3]:
P(2 ≤ x ≤ 3) = ∫2^3 f(x) dx
= ∫2^3 (1/4) dx
= (1/4) [x]2^3
= (1/4) (3-2)
= 1/4
Therefore, the probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.
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Need help pleaaasseee
By using chi-squared test, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.
What is chi-squared test?
To perform a chi-squared test for independence between breed and milk yield, we need to set up the hypotheses:
Null hypothesis: There is no association between breed and milk yield.
Alternative hypothesis: There is an association between breed and milk yield.
We will use a significance level of 0.05.
To calculate the expected counts for each cell, we will use the formula: (row total x column total) / grand total.
The observed counts and expected counts are:
The grand total is 100.
The degrees of freedom for the test are (number of rows - 1) x (number of columns - 1) = (2 - 1) x (3 - 1) = 2.
Using a chi-squared distribution table or calculator, we find the critical value for a chi-squared test with 2 degrees of freedom and a 0.05 significance level to be 5.99.
To calculate the test statistic, we use the formula:
chi-squared = [tex]sum((observed\ count - expected\ count)^2 / expected\ count)[/tex]
The calculated value of chi-squared is:
[tex]chi-squared = ((32-25.76)^2 / 25.76) + ((20-19.04)^2 / 19.04) + ((16-13.20)^2 / 13.20) + ((10-16.24)^2 / 16.24) + ((18-18.96)^2 / 18.96) + ((4-4.80)^2 / 4.80) = 10.92[/tex]
The degrees of freedom for the test are 2, and the critical value is 5.99.
Since the calculated value of chi-squared (10.92) is greater than the critical value (5.99), we reject the null hypothesis.
Therefore, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.
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The area of a parallelogram with base b and height h is bh. Greta is using tiles shaped like parallelograms to cover her bathroom floor. Each tile has a 4.25-inch base and is 2 inches high.
What is the area of each tile?
Write your answer as a whole number or decimal.
Answer:
Each tile would be 8.5 in
Step-by-step explanation:
Area of parallelogram is A=bh, so 4.25*2= 8.5
Help me please anyone ?!!!!?!!
Answer:
Its b,
Step-by-step explanation:
I had this test before i chose b and it was right
Answer:
(1, 6), (2, 12), (3, 18), (4, 24)
Which function represents the exponential graph given that (0, 1) and (4, 81/16 ) are points that lie on the graph?
f(x)=(2/3)^x
f(x)=(4)^x
f(x)=(1)^x
f(x)=(3/2)^x
The f(x) = (3/2)ˣ is the correct function that represents the given exponential graph.
What is exponential graph?An exponential graph is a type of graph that represents an exponential function. An exponential function is a mathematical function in which a constant base is raised to a variable exponent. The general form of an exponential function is: y = a * bˣ.
What is graph?A graph is a visual representation of data or information that allows us to quickly and easily understand patterns, trends, and relationships. Graphs are used to present information in a way that is easy to interpret and understand.
In the given question,
The function that represents the exponential graph given that (0, 1) and (4, 81/16 ) are points that lie on the graph is:
f(x) = (3/2)ˣ
To verify that this is the correct function, we can substitute x=0 and x=4 into the function to see if the corresponding y-values match the given points on the graph.
When x=0, f(0) = (3/2)⁰ = 1, which matches the point (0, 1).
When x=4, f(4) = (3/2)⁴ = 81/16, which matches the point (4, 81/16).
Therefore, f(x) = (3/2)ˣ is the correct function that represents the given exponential graph.
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A woman weighing 130 lbs drinks 2 mixed drinks (2 oz of liquor mixed with soda) with
dinner between 7-8 pm. At 10 pm she had a glass of wine.What was her BAC at 8 pm?
Answer:
Step-by-step explanation:
The BAC (Blood Alcohol Concentration) of a person depends on several factors, such as the amount of alcohol consumed, the time over which the alcohol was consumed, and the weight and gender of the person. For this problem, we will assume that the woman has a normal metabolism and that the alcohol is completely absorbed into her bloodstream.
To calculate the BAC at 8 pm, we need to know the amount of alcohol that the woman consumed and the time over which she consumed it. We are given that she had 2 mixed drinks between 7-8 pm, which contained a total of 2 ounces of liquor. We are also given that she had a glass of wine at 10 pm, but we don't need to consider this for the BAC at 8 pm.
Using the Widmark formula, we can calculate the BAC at 8 pm:
BAC = (Alcohol consumed / (Body weight x r)) - (0.015 x Hours since first drink)
where r is the gender constant (0.55 for females) and 0.015 is the rate at which the liver metabolizes alcohol.
Plugging in the values we know, we get:
BAC = (2 oz / (130 lbs x 0.55)) - (0.015 x 1 hour)
BAC = 0.0208 - 0.015
BAC = 0.0058
Therefore, the woman's BAC at 8 pm was approximately 0.0058, which is below the legal limit for driving in most states in the US.
Question 7
Suppose the graph represents the scale drawing for a fence that Tara is building for a new city dog park. Each unit on the graph represents 12 yards. After studying the scale drawing, Tara decides to build a fence that encloses a smaller area. If Tara dilates rectangle ABCD by a scale factor of 0.75, and fencing costs $6.39 per yard, how much will she spend on fencing?
The total cost to fence the rectangular yard is given as follows:
$1,610.28.
How to obtain the perimeter of a triangle?The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.
If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:
P = 2l + 2w
Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:
0.75 x 12 = 9 yards.
Hence the dimensions of the rectangle are given as follows:
Length of 8 x 9 = 72 yards.Width of 6 x 9 = 54 yards.The perimeter of the fence is then given as follows:
2 x (72 + 54) = 252 yards.
It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:
252 x 6.39 = $1,610.28.
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Help with math problems
The inequality can be solved to get 2 > x, and the graph on the number line can be seen in the image at the end.
How to solve the inequality?Here we have an inequality and we want to sole it, to do so, we just need to isolate the variable in the inequality.
Here we have:
10 > 5x
To isolate the variable we can divide both sides of the inequality by 5, then we will get:
10/5 > 5x/5
2 > x
So x is the set of all values smaller than 2.
That is the inequality solved, to graph this, drawn an open circle at x = 2 and a line that goes to the left. The graph is the one you can see in the image below.
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