Express the statement as an inequality.
(a) x is negative.
x ≥ 0
x > 0
x < 0
x = 0
x ≤ 0
(b) y is nonnegative.
y < 0
y ≥ 0
y = 0
y ≤ 0
y > 0
(c) q is less than or equal to .
q <
q ≤
q >
q =
q ≥
(d) d is between 2 and 1.
1 ≤ d ≤ 2
d < 1 < 2
2 ≥ d ≥ 1
1 < d < 2
1 < 2 < d
(e) t is not less than 5.
t ≥ 5
t > 5
t = 5
t < 5
t ≤ 5
(f) The negative of z is not greater than 3.
z ≤ −3
−z ≤ 3
z < 3
−z < 3
z ≤ 3
(g) The quotient of p and q is at most 6.
p/q < 6
p/q = 6
p/q > 6
p/q ≤ 6
p/q ≥ 6
(h) The reciprocal of w is at least 9.
1/w < 9
1/w ≥ 9
1/w ≤ 9
1/w > 9
1/w = 9
(i) The absolute value of x is greater than 6.
|x| ≥ 6
|x| ≤ 6
|x| = 6
|x| > 6
|x| < 6
The expression of the inequality word problems for each question is; As expressed below
How to express inequalities?A) x is negative. This can be expressed as;
x < 0
B) y is non-negative. This can be expressed as;
y > 0
C) q is less than or equal to is expressed as; q ≤
D) d is between 2 and 1 is expressed as 1 < d < 2
E) t is not less than 5 is t ≥ 5
F) The negative of z is not greater than 3 is expressed as;
−z ≤ 3
G) The quotient of p and q is at most 6 is expressed as; p/q ≤ 6
H) The reciprocal of w is at least 9 is 1/w ≥ 9.
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(OAU
29 Mike knows that (3,6.5) and (4,17.55) are points on the graph of an exponential function, g(x), and
he wants to find another point on the graph of this function.
First, he subtracts 6.5 from 17.55 to get 11.05.
Next, he adds 11.05 and 17.55 to get 28.6.
He states that (5,28.6) is a point on g(x).
Is he correct? Explain your reasoning.
Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect
How to determine if he is correct?The points are given as:
(3,6.5) and (4,17.55)
An exponential equation is represented as:
[tex]y = ab^x[/tex]
Using the given points, we have the following equations:
[tex]ab^3 = 6.5[/tex]
[tex]ab^4 = 17.55[/tex]
Divide both equations:
[tex]ab^4 \div ab^3 = 17.55 \div 6.5[/tex]
Evaluate
b = 2.7
Substitute b = 2.7 in [tex]ab^3 = 6.5[/tex]
[tex]a * 2.7^3 = 6.5[/tex]
Solve for a
[tex]a = \frac{6.5}{2.7^3}[/tex]
Substitute [tex]a = \frac{6.5}{2.7^3}[/tex] and b = 2.7 in [tex]y = ab^x[/tex]
[tex]y = \frac{6.5}{2.7^3} * 2.7^x[/tex]
His point (5,28.6) means that:
x = 5 when y = 28.6
Substitute x = 5 in [tex]y = \frac{6.5}{2.7^3} * 2.7^x[/tex]
[tex]y = \frac{6.5}{2.7^3} * 2.7^5[/tex]
Evaluate
y = 47.385
y = 47.385 and y = 28.6 are not the same
Hence, Mike's claim is incorrect
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a quadrilateral is inscirbed in circle o. the angle measures the quadrilateral in degrees are given by the expressions shown in the figure.
what is the measure of angle c?
(will mark branliest + 20points)
Answer:
A. 65 degrees
Step-by-step explanation:
The required measure of the angle c in the quadrilateral is given as 65°.
As mentioned in the question,
A quadrilateral is inscribed in a circle o. the angle measures the quadrilateral in degrees is given by the expressions shown in the figure.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
In a quadrilateral, the sum of the composite angle is equal to 180°,
∠A + ∠C = 180
130 -x + 95 -2x = 180
-3x = 180 - 225
x = 15
Now,
∠c = 95 - 2x
∠c = 95 - 2×15
∠c = 65
Thus, the required measure of the angle c in the quadrilateral is given as 65°.
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A box has candies in it: are taffy, are peppermint, and are caramel. (Each candy falls into only one of these categories.) Brian wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the first candy selected is taffy and the second candy is caramel?
Do not round your intermediate computations. Round your final answer to three decimal places.
Probability that the first candy selected is taffy and the second candy is caramel is 0.144.
The data missing in the question is
A box has 18 candies in it: 3 are peppermint, 4 are caramel, and 11 are taffy.
What is Probability ?Probability can be defined as the study of likelihood of an event to happen.
It has a range of 0 to 1.
Probability is the ratio of the expected outcomes / total coutcome.
Total outcomes = 18
The probability that the first candy is taffy is 11/18
Now as there is no replacement , the total outcomes can be 17
The probability that the second candy is caramel is 4/17
Probability that the first candy selected is taffy and the second candy is caramel = (11/18)(4/17)
= 0.144
Therefore the Probability is 0.144
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Line segment JM has endpoints with coordinates -2 and 14 on a number line. Points K and L are on segment JM. K has a coordinate of 2 and point L has a coordinate of 8. Find the probability that a point on JM is placed first on JL and a second point is not placed on KL.
5/8
25/64
15/64
8/15
Answer:
25/64Step-by-step explanation:
consider the events F and S :
F : «the first point is placed on JL»
S : «the second point is not placed on KL»
F∩S : «a point on JM is placed first on JL and a second point is not placed on KL»
[tex]p\left( F\right) =\frac{JL}{JM} =\frac{10}{16} =\frac{5}{8}[/tex]
[tex]p\left( \overline{S} \right) =\frac{KL}{JM} =\frac{6}{16} =\frac{3}{8}[/tex]
[tex]\Longrightarrow p\left( S\right) =1-p\left( \overline{S} \right) =1-\frac{3}{8} =\frac{5}{8}[/tex]
[tex]p\left( F\cap S\right) =p\left( F\right) \times p\left( S\right) =\frac{5}{8} \times \frac{5}{8} =\frac{25}{64}[/tex]
A board game uses a deck of cards that players draw from to move tokens around the board. The probability of selecting a card that moves a player's token forward is 32%. Over the course of a game, the deck is shuffled and reused as necessary. Approximately how many cards must be drawn from the deck before players' tokens move forward 50 times?
Using the binomial distribution, it is found that approximately 156 cards must be drawn from the deck before players' tokens move forward 50 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected number of trials until q successes is:
[tex]E_s(X) = \frac{q}{p}[/tex]
In this problem, the parameters are given as follows:
q = 50, p = 0.32.
Hence:
[tex]E_s(X) = \frac{50}{0.32} = 156[/tex]
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L=24 B=12 area=______
Perimeter=_______
Answer:
Area= 288
Perimeter= 72
Step-by-step explanation:
In order to get the area of a rectangle, you multiply the length by the width, 24x12=288.
In order to find the perimeter just add all of the sides, there are 2 sides with a length of 24, and two sides with a width of 12.
24+24+12+12=72
Can someone please explain how the answer to this is, "19 and 3", "1 and 12"
Using the image given, the angles that are Alternate Exterior Angles are: 1, 2, 3, 4,13,14, 18, 19.
What are Alternate Exterior Angles?These are known to be the Alternate exterior angles that are regarded as the pair of angles found on the outer side of the two parallel lines but they are seen on the opposite side of the transversal.
Note that in the image given, there are two parallel lines and two transversal lines.
Note also that to get the Alternate exterior angles, it has to be the angles seen on the seen on the opposite side of the transversal that has crossed the parallels lines and from the image given, only angle 1, 2, 3, 4,13,14, 18, 19 fit into the description.
Therefore, Using the image given, the angles that are Alternate Exterior Angles are: 1, 2, 3, 4,13,14, 18 19.
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Which smallest number is subtracted from the number 12675 to make it a perfect square?
what is the range of exponential function f(x)=9*2^x
Answer:
uhm smhtn
Step-by-step explanation:
i really just want points.
Answer:
(0,infinity)
Step-by-step explanation:
.
Solve the equation for x.
√x+5 -1 = 2
Answer:
Step-by-step explanation:
Equation
√(x + 5) - 1 = 2 I take it that you want the 5 to be with the x.
Solution
√(x + 5) - 1 = 2 Add 1 to both sides
√(x + 5) - 1 +1 = 2 + 1 Combine
√(x + 5) = 3 Square both sides
√(x + 5)² = 3² Combine
x + 5 = 9 Subtract 5 from both sides
x + 5- 5 = 9- 5
x = 4
Answer x = 4
there are 20 students 15 men and 5 women in a maths class,in how many different ways can a committee of 3 men and 2 women be choosen
[tex]\displaystyle\\\binom{15}{3}\cdot\binom{5}{2}=\dfrac{15!}{3!12!}\cdot\dfrac{5!}{2!3!}=\dfrac{13\cdot14\cdot15}{2\cdot3}\cdot\dfrac{4\cdot5}{2}=13\cdot7\cdot5\cdot2\cdot5=4550[/tex]
6 kids play a tennis game. Each play each other once. How many games did they play altogether
Help ASAP! Please this is hard!
A bag contains 15 red candies, 15 yellow candies, and 15 blue candies. What is the probability of randomly
choosing two candies of the same color, without replacement?
[tex]|\Omega|=45\cdot44=1980\\|A|=15\cdot14\cdot3=630\\\\P(A)=\dfrac{630}{1980}=\dfrac{7}{22}\approx31.8\%[/tex]
Umberto plants a garden with an area of 16 square feet. What is the area of the garden in square inches
Answer:
2,304 inches
Step-by-step explanation:
1 square foot = 144 square inches
16 x 144 = 2,304 square inches
pls help, thank you!!
Answer: 1, 3
For a cubic polynomial, there are either 3 real roots or 1 real root nad 2 complex roots in a conjugate pair.
Find the value of x.
5+x=7
x = [?]
Answer:
x = 2Step-by-step explanation:
Find the value of x.
5+x=7
x = [?]
5 + x = 7
x = 7 - 5
x = 2
----------------check
5 + 2 = 7
7 = 7
the answer is good
i will mark as brainiest
If two triangles are similar, then their side lengths are proportional.
RS / JK = RT / JL
5 / x = 4 / 7
4x = 35
x = 35/4 = 8.75
RT / JL = TS / LK
4 / 7 = 6 / (y + 2)
42 = 4(y + 2)
42 = 4y + 4
4y = 38
y = 38/4 = 9.5
LK = 9.5 + 2 = 11.5 cm
JK = x = 8.75
Hope this helps!
What is the value of F(x)=-x+9 if x=-7
Answer: F = - 2/7
Step-by-step explanation:
[tex]f(x) = x + 9\\f(-7) = -7 + 9\\f(-7) = 2\\f = -\frac{2}{7}[/tex]
Find the missing side of this right
triangle.
30
X
[?]
X = 1
Enter the number that belongs in the green box.
Answer:
see the attachment photo!
1/2 inch represents a distance of 1/8 mile.her house is two miles away from school
Answer:
1/6
Step-by-step explanation:
the answer is 1/6th use subtraction
Jannet walked 1 2/3 of a mile and her brother jamie walked 2 4/5 of a mile. How much did they walk all together
Answer:
4 7/15 miles
Step-by-step explanation:
1 2/3 + 2 4/5
Make alike denominators by multiplying 1 2/3 by 5 and 2 4/5 by 3
1 10/15 + 2 12/15 = 3 22/15
4 7/15 miles altogether that was walked
Give brainliest please!
Hope this helps :)
11+22+33+44+55+66+77+88+99+110+220+330+440+550+660+770+880+990+1110=
Answer:
6545
Step-by-step explanation:
i spent time on this. i had to type out everything. by. hand.
see calculator image for proof. enjoy.
Answer: 6,555 im good at trig and using the pythagorean therum
Step-by-step explanation: brainliest?
Please solve the whole page please please
1d) ↑ (Do the same but turned if that's easier)
1a) 199
1b) 193
1c) 217
1e) Based on the box plot, we can for example, find the lowest and greatest values, the range (largest - smallest), the mean (all values / # values), and the median middle value or q2 given by the second line in the box.
2b) 7
2c) 9.5
2d) ↑
2e) because the data is not ordered, it is difficult to determine the quartile data. Once it is ordered like 6, 7, 7, 7, 8, 8, 9, 10, 10. The data can be visualized alot easier. With the box plot we can determine q3 of the data by looking at the 3rd line, using the whiskers of the box to find the minimum and maximum values.
3)
You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.
In this case the ordered data would be: 4,6,8,8,9,11,12,14,14,16.
[4, 6, 8, 8, 9] [] [11, 12, 14, 14, 16]
4 is the minimum, 16 is the maximum, q1 is 8, q3 is 14, and median is 10.
4) ↑
5)
You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.
In this case the ordered data would be:
45, 45, 50, 55, 60, 70, 70, 75, 80, 85
[45, 45, 50, 55, 60] [] [70, 70, 75, 80, 85]
45 is the minimum, 85 is the maximum, q1 is 50, q3 is 75, and median is 65.
6) ↑
8 3/8 + 3 3/8 + 2 3/8 + 3/8
what is the answer of this ?
The simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have an expression:
[tex]= 8 \dfrac{3}{8} + 3 \dfrac{3}{8} + 2 \dfrac{3}{8} + \dfrac{3}{8}[/tex]
After simplification:
[tex]= \dfrac{67}{8} + \dfrac{27}{8} + \dfrac{19}{8} + \dfrac{3}{8}[/tex]
[tex]= \dfrac{67+27+19+3}{8}[/tex]
= 116/8
= 29/2
[tex]= 14\dfrac{1}{2}[/tex]
Thus, the simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
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Answer:
i dont understand your question
Step-by-step explanation:
2. A function fis given by f: x→ 5x-8, where x € R. Find
a. f(-4)
b. the value of x whose image is 12
Answer:
a. -28b. 4Step-by-step explanation:
f: x→ 5x-8
a. f(-4) = 5(-4) - 8 = -20 - 8. = -28
b. the value of x whose image is 12
To find the value of x ,we have to solve f(x) = 12
f(x) = 12
⇔ 5x-8 = 12
⇔ 5x = 12 + 8
⇔ 5x = 20
⇔ x = 20 ÷ 5 = 4
Solve the radical equation.
√x+3-1= x
Answer:
x = 1
Step-by-step explanation:
Radical expression:
√(x+3)-1 = xLet's find the value of x.
Solved:
√(x+3)-1 = x
Transpose -1 to RHS:
=> √(x+3) = x+1Squaring both LHS and RHS,we have:
=> √(x+3)^2= (x+1)^2 => x+3 = x²+2x+1Subtracting x^2+2x+1 from both sides,we have:
=>x+3−(x²+2x+1)=x²+2x+1−(x²+2x+1)=> −x^2−x+2=0Factoring LHS,we have:
=>(−x+1)(x+2)=0Setting (-x+1) = 0 and (x+2) = 0 each time:
=>(-x+1) = 0=> x-1 = 0=> x = 0+1=> x=1Now
=> (x+2) = 0=> x= 0-2=> x = -2There are two solutions– (1,-2)
Let's plug to the given equation to check.
x = 1 :√(x+3) -1 = x
√(1+3)-1 = 1√4 - 1 = 12 - 1 = 11 = 1Equation is true,when plugged to x = 1.
x = -2:√(x+3) -1 = x
√(2+3) - 1 = -2√5 -1 = -22.23606 - 1 = -21.236 = -2Equation is false,when plugged to x = -2.
Hence,the value of x is 1.
-Regards,Hannah
Present a picture of an object (TV, Ipad Screen, Book Cover) that contains a right angle (it could be something in nature or that is man-made). Use a ruler or measuring tape to measure the two sides that make the right angle and measure the distance from the end of one side to the end of the other side (hypotenuse). Draw a diagram of the object including the measurements. Use your leg measurements on your diagram to calculate a theoretical hypotenuse. (Show all steps).
The measure of hypotenuse using the ruler is 25.5 cm and using the formula is 23.43 cm, they are not same, and formula can be used to in the real life problems as well.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The question is incomplete:
The complete question is:
Present a picture of an object (TV, Ipad Screen, Book Cover) that contains a right angle (it could be something in nature or that is man-made). Use a ruler or measuring tape to measure the two sides that make the right angle and measure the distance from the end of one side to the end of the other side (hypotenuse). Draw a diagram of the object including the measurements. Use your leg measurements on your diagram to calculate a theoretical hypotenuse. (Show all steps).
Does the hypotenuse that measured with a ruler/measuring tape equal the hypotenuse you calculated?Why do you think they are or are not exactly the same?What did you learn from developing this presentation?
We are assuming the length of one side x:
x = 18 cm
Length of other side y:
y = 15 cm
And length of the hypotenuse z:
z = 23.5 cm
From the Pythagoras theorem:
z² = x² + y²
z² = 18² + 15²
z² = 549
z = √54 = 23.43 cm
The measure of hypotenuse is:
Using ruler: x = 25.5 cm
Using formula: x = 23.43 cm
They are not equal due to the reading in the ruler.
The formula can be used to in the real life problems as well.
Thus, the measure of hypotenuse using the ruler is 25.5 cm and using the formula is 23.43 cm, they are not same, and formula can be used to in the real life problems as well.
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The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.
Speed
(s kilometres per hour) Frequency
40 < s 50 10
50 < s 60 16
60 < s 70 19
70 < s 80 23
80 < s 90 12
(a) Write down the modal class
(b) Work out an estimate for the mean speed of the motorbikes as they pass under the bridge.
Give your answer correct to 3 significant figures.
The modal class is 70 - 80 and the mean speed is 66.4
How to determine the modal class?The table of values is given as:
Speed Frequency
40 - 50 10
50 - 60 16
60 - 70 19
70 - 80 23
80 - 90 12
The modal class is the class with the highest frequency
The class 70 - 80 has the highest frequency of 23
Hence, the modal class is 70 - 80
How to determine the mean?Rewrite the frequency table to include the class midpoints
x f
45 10
55 16
65 19
75 23
85 12
The estimate of the mean speed is then calculated as:
[tex]\bar x =\frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{45* 10 + 55 * 16 + 65 * 19 + 75 * 23 + 85 * 12}{80}[/tex]
Evaluate
[tex]\bar x = 66.4[/tex]
Hence, the mean speed is 66.4
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