The sum of 2 and b is greater than or equals to -27 is expressed as 2 + b ≥ -27. Therefore, b ≥ -29
How to represent words expression to mathematical expression?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Therefore, let's convert the words expression to a mathematical expression(inequality).
The sum of 2 and b is greater than or equals to -27 can be expressed as follows:
2 + b ≥ -27
Let's solve for b
2 + b ≥ -27
subtract 2 from both sides of the inequality
2 - 2 + b ≥ -27 - 2
b ≥ - 29
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rachel is going to calculate the following expression: $\frac{3.32}{1.66} 18.4$. she calculates the expression as it is written and then writes down the answer rounded to the nearest whole number. she then calculates it again, but rounds each of the 3 numbers in the expression to the nearest integer, and then performs the division and addition. she writes this answer down next to the answer she got before. what is the positive difference between the 2 answers she got?
The positive difference between the two answers is 8.6 units.
Rachel first calculates the expression as it is written and rounds the answer to the nearest whole number:
$\frac{3.32}{1.66} 18.4$ = 18.4
She then calculates it again, but rounds each of the 3 numbers in the expression to the nearest integer:
$\frac{3}{2} 18$ = 27
The positive difference between the two answers is:
18.4 - 27 = -8.6
So, the positive difference between the two answers is 8.6 units.
It's worth noting that when you round the numbers before performing the calculations, the result may be different than the exact result, but it can be useful in some cases to have an approximation of the answer.
Also, the difference between the two answers is negative because the second answer is greater than the first one.
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How do you translate a line graph?
The graph of a linear function (a line) can be moved around the coordinate grid. This is called a transformation. There are three basic transformations: translation (sliding the line around), reflection (flipping the line), and scaling (stretching the line). You can move (transform) the line vertically or horizontally.
Now, According to the question:
Transformations of Graphs:
Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis. A graph is translated k units horizontally by moving each point on the graph k units horizontally.
The graph of a linear function (a line) can be moved around the coordinate grid. This is called a transformation. There are three basic transformations: translation (sliding the line around), reflection (flipping the line), and scaling (stretching the line). You can move (transform) the line vertically or horizontally.
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What is the slope of any line parallel to Y =- 3x 7?
When we compare the given expression with the slope-intercept form, we get the required slope. Here, the slope is -3.
A line's slope or gradient numerically expresses its steepness and direction. It provides the ratio of how much y alters when x alters by a particular amount. Since m is the slope and c is the y-intercept, y=mx+c is the general form. This is the slope-intercept form.
Compare the given expression y=-3x-7 with the slope-intercept form. We get, the slope value as m=-3 and the intercept value as c=-7. Therefore, the required answer is -3. So the value of y changes with -3 times of x.
The complete question is -
What is the slope of any line parallel to y=-3x-7?
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The scale of a map is 1 inch equals 40 miles how many actual miles does 0.65 inches represent
A distance of 6.5 inches on the map represents 6.5*40 = 260 miles on the ground.
how many actual miles does 0.65 inches represent?step1:
scales on a map =40 inch .
1 inch =40 miles .
then miles represents on the map =6/1/2 .
6/1/2=40miles .
13/2=40
80=13,
scale on the map =3/13/42
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On a ground-based map, 6.5 inches correspond to 6.5*40, or 260 miles.
How can I tell what a map's scale is?The legend for the map includes a scale bar. It is stated as an inch-to-inch, foot-to-foot, or mile-to-mile conversion of the ground to the map.
The relationship (or ratio) between the distances shown on a map and their actual distances on the ground is referred to as the map scale.
40 inch is the scale of a map.
1 inch equals 40 miles.
then miles on the map is represented as 6/1/2, which is 40 miles.
13/2 = 40 80 = 13, and the map's scale is 3 13/42.
On a ground-based map, 6.5 inches correspond to 6.5*40, or 260 miles.
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A card from the set below is chosen at random.
What is the probability of drawing a card with stripes?
P (stripes)
(HELP, DUE IN AN HR!!)
Answer: 4/12
Step-by-step explanation: Simplified into 1/4 :)
Answer:
4/12 chance of getting striped card
Step-by-step explanation:
There are 4 striped cards, out of 12 cards, so that would be 4/12
A 16-cup jug of water costs $3.52. What is the price per quart?
The price per quart of water would be = $2.35
What is equivalent of a quart?The equivalent of a quart means the total amount of cups of water that can be found in a quart after conversation.
The equivalence of a quart of water would be = 4 cups
Therefore, if 6 cups = $ 3.52
4 cups = X
Make X the subject of formula;
X = 4 × 3.52/6
X = 14.08/6
X = 2.35
Therefore, a the price per quart of water = $2.35.
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sixty subjects were randomly divided into two groups to study the effects of alcohol on reaction time. the members of one group consumed a specified amount of alcohol, and members of the other group had a nonalcoholic beverage. the reaction time of both groups were measured before and after the beverage. a) what is the response variable? b) what is the treatment? c) what is an experimental unit? d) what is the purpose of one group drinking a nonalcoholic beverage? e) are any extraneous variables possible confounded with the treatment? if yes, identify and explain. f) is this study an observational study or an experiment? explain
One albino laboratory rat is an independent variable.
To investigate how alcohol affects reaction times, sixty participants were randomly split into two groups. Those in one group drank a certain amount of alcohol, while those in the other group drank non-alcoholic beverages. Both groups' reaction times were timed before and after the beverage.
A variable that is independent is one that is capable of standing alone.The independent variable is unaffected by other variables and remains unchanged at all times.Although the other elements may be out of the ordinary, it still stands on their own.A person's age, for instance, is an independent variable.Know more about reaction time
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The question is incomplete and wrong:
Sixty albino laboratory rats were randomly divided into two groups as part of a study on the effects of alcohol on reaction time. Each member of one group consumed a specified amount of alcohol and members of the other group had a non-alcoholic beverage. The reaction time of both groups was measured before and after taking the beverage/alcoholic drink. What is the INDEPENDENT VARIABLE?
a. Amount of alcohol
b. Reaction time
c. One albino laboratory rat
d. Sixty albino laboratory rats
At a local
preschool, there is a ratio of 3
boys to every 4 girls. If there are 245 total
preschoolers enrolled, then how
boys?
many are
Answer:
There are 105 boys in preschool.
Step-by-step explanation:
We can set an equation:
(boys/girls)=3/4;
boys + Girls = 245
We know that Boys = 3/4* Girls
substitute it into the second equation:
3/4* Girls + Girls = 245
(3/4 + 1) * Girls = 245
(7/4)Girls = 245
Girls = 2454/7
Girls = 140
So there are 140 girls in preschool.
Now we can use the ratio of boys to girls (3:4) to find the number of boys:
boys = (3/4) * 140 = 105
There are 105 boys in preschool.
100 POINTS, PLEASE HELP, WILL GIVE BRAINLEIST
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
What is the domain of the relation?
{−3, −2, −1, 0, 1, 2, 4}
{−3, 0, 1, 4}
{−2, −1, 0, 1, 4}
{−3, −1, 0, 2, 4}
Answer: { -3, -1, 0, 2, 4}
Step-by-step explanation:
the domain is the x values of ordered pairs
U and X are the midpoints of the legs,
TV
and
SW
, of trapezoid STVW.
If ST=p, UX=4p–83, and VW=2p+9, what is the value of p?
The value of the side ST or p is equal to 3
What is Trapezoid?A trapezoid is also known as a trapezium is a four-sided polygon or a quadrilateral. It has one set of opposite sides which are parallel and a set of non-parallel sides. The parallel sides are known as the bases and the non-parallel sides are known as the legs of the trapezoid.
Given here: A trapezoid STVW and ST=p and UX=4p-3 and VW=2p+9 with U and X are midpoints.
The length of the midsegment is the sum of the two bases divided by 2.
Now we know that the mid segment UX is given by
UX= ST+VW / 2
thus substituting the values we get
4p-3= p+2p+9 /2
8p-6=3p+9
5p=15
p=3
Hence, The value of p is equal to 3
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please help me with this angles question
The values of angles x and y in the trapezium are 48 and 115 degrees.
How to find the angles of a trapezium?A trapezium is a quadrilateral with one pair of sides parallel to each other. Sum of angles pair between parallel line is 190 degrees.
Therefore, let's find x and y in the trapezium.
y + 132 = 180
subtract 132 from both sides of the equation
y + 132 - 132 = 180 - 132
y = 48 degrees
x + 65 = 180
subtract 65 from both sides of the equation
x + 65 - 65 = 180 - 65
x = 115 degrees.
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Solve
(-6 - 4) ÷ (-5) =
(A) 24.2
(B) -2
(C) -24.2
(D) 2
Answer: D
Step-by-step explanation:
(-6-4) / (-5)
= -10/-5
=10/5
=2
=D
Answer: -2
Step-by-step explanation: From the question
(-6 - 4) ÷ (5)
-10 ÷ 5
The answer is -2
Explain whether there is enough information given in the figure to prove that the triangles are congruent using SSS or SAS
The triangles are congruent using SSS or SAS, *for 8* Yes, SAS says it is accurate.
How does SSS demonstrate the congruence of a triangle?According to the SSS rule, two triangles are said to be congruent if each of their three sides is equal to each of their respective three sides in the second triangle.All that is left to do is demonstrate that MP is congruent to MP since we already know that LM and NM are congruent as well as that angles LMP and NMP are congruent. To do this, we may use the reflexive property to claim that MP is congruent to MP.Two triangles are said to be congruent if they have two sets of congruent sides and the included angle, according to the SAS criterion for triangle congruence (the one between the congruent sides).To learn more about congruent refer to:
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What is the slope of the line passing through the points (- 9 3 and 7 7?
The slope of the line passing through the points (- 9, 3) and (7, 7) is 1/4.
In the given question we have to find the slope of the line passing through the points (- 9, 3) and (7, 7).
The formula for finding the slope of line is
m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
The given points are (- 9, 3) and (7, 7).
From the given point;
x(1) = -9, y(1) = 3, x(2) = 7, y(2) = 7.
Now putting the value in the formula
m = [tex]\frac{7-3}{7-(-9)}[/tex]
m = [tex]\frac{4}{7+9}[/tex]
m = [tex]\frac{4}{16}[/tex]
m = 1/4
Hence, the slope of the line passing through the points (- 9, 3) and (7, 7) is 1/4.
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The complete question is:
What is the slope of the line passing through the points (- 9, 3) and (7, 7)?
just two more questions yall
Answer:
30°
Step-by-step explanation:
refer to the attachment for your answer.
Hope this helps!
-Rishabh
Answer: The answer is X = 30
Step-by-step explanation:
I mostly just did the "guess and check" method until I got 30, this answer seemed right, here are the angle measurements as well:
For 4(x)-16, I put 30 in for x, solved using basic arithmetic, and the angel comes out to be 104 degrees.
For 2(x)+16, I put 30 in for x, did basic arithmetic again, and the angel came out to be 76 degrees.
PLEASE HELP ME I NEED THIS ASAP WIll MARK BRAINLIEST!!!!
10. What is the value of x in the figure shown below?
P
89⁰
Q
44°
Respond in the space provided.
to
R
Answer: x=68
Step-by-step explanation:
The triangle equal up to 180 and 89 + 44 = 128
And 128 - 180 is 68
So x=68
Hope this help Please make me as the brainlest.
AABC is a dilation of ADEF with center (0, 0). What is the scale factor?
1/3
1/2
3
1/4
The scale factor of AABC dilation of ADEF with center (0, 0) is 3.
What is scale factor?Scale factor is a numerical value used to indicate the proportional change in the size of an object or image. It is often expressed as a fraction or ratio, for example 1:2, where the first number (1) represents the original size, and the second number (2) represents the new size. This is also referred to as a "scaling factor," since it indicates how much larger or smaller the new size is compared to the original size. Scale factors can be used to resize objects in different directions, such as width, height, and depth.
This means that each point of ADEF was scaled up by a factor of 3. This means that the length and width of ADEF were multiplied by 3 to make the new figure AABC. For example, if the length of ADEF was 6, then the length of AABC would be 18. Similarly, if the width of ADEF was 9, then the width of AABC would be 27.
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Mary can make 4 bracelets every 10 minutes . How many minutes would it take for Mary to make 20 bracelets ?
Answer: 50 minutes
Step-by-step explanation:
4 bracelets for 10 minutes
20/4=5
5*10=50
so it will take them 50 minutes
Answer: 50 minutes for 20 bracelets
Step-by-step explanation: 4 × ?=20
4 × 5 = 20
now we could add 10+10+10+10+10=50
or
we could multiply 10 by 5.
we would get 50.
Hope this helps!
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What is the range of f/x )= x²?
The range of f(x)= x² is [0, +∞) or the set of all non-negative real numbers.
The range of a function is the set of all possible output values (y-values) for the function.
To determine the range of the function f(x) = x², plug in some values for x:
If x = 0, then f(x) = 0² = 0, which is a non-negative real number.
If x = 1, then f(x) = 1² = 1, which is a non-negative real number.
If x = -1, then f(x) = -1² = 1, which is a non-negative real number.
For any real number x, x² is always non-negative, so the range of the function is all non-negative real numbers [0, +∞).
Alternatively, we can also see that the parabola of the function opens upward and the vertex is at the origin. Therefore, the range of the function is all non-negative real numbers.
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Constant Variance Definition
Constant variance is the assumption of regression analysis that the standard deviation and variance of the residuals are constant for all the values of variables that are independent.
Constant variance is the assumption of regression analysis that the standard deviation and variance of the residuals are constant for all the values of variables that are independent. - This statement is correct.
Homogeneity of variances means the assumption that the variances of the random variables are constant. This homoscedasticity (that is, constant variances) assumption can be tested using the same diagnostics used for linear regression models.
All data usually consist of the dependent variable and the independent variable itself. Constant variance is about many linear regression assumptions. For example, if you have 325 rows, there should be at least one variance, possibly a constant.
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Four Questions for 80 points
1. Each side of the base of a square pyramid measures 10 inches. The height of each lateral face of the pyramid is also 10 inches.
What is the surface area of the pyramid?
Enter your answer in the box.
2. A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches.
What is the surface area of the pyramid?
Enter your answer in the box
3. A child's toy is in the shape of a square pyramid. The pyramid stands 20 inches tall and each side of the base measures 24 inches.
Half of the surface area of the pyramid is black and the remainder is yellow.
What is the surface area of the toy that is yellow?
Enter your answer, rounded to the nearest tenth, in the box.
4. Question
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 50 feet and the slant height of each lateral side of the pyramid is 40 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.
Answer: 1. 323.6
Step-by-step explanation:
Refer to diagram shown
The measure of <HMG is 40 degree.
What is Angle Sum Property?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Given:
In triangle HJL
HJ = HL (given)
let <HJL = <HLJ= 75 (Angles opposite to equal side also equal)
Using Angle Sum property in HKL
75 + 90 + <KHL = 180
<KHL = 180 - 165
<KHL = 15
Now, in Triangle HKM
<KHM = 35 + 15 = 50
So, Using Angle Sum property
50 + 90 + <HMK = 180
<HMK = 180- 140
<HMK = 40
Hence, the measure of <HMG = 40 degree.
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what is the answer please help me quickly!!!
The additional amount of money Dan will spend can be written in an inequality form such as = c >/= $15
What is inequality?Inequality is defined as the expression that is used to represent two values that are not equal. < less than or > great than signs are usually used for such expressions.
The least amount of money Dan can spend of gifts = $32
The amount he has spent so far = $15
The amount remaining c = 32-15 = $17
Therefore, additional amount of money Dan will spend can be written in an inequality form such as = c >/= $15
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A box in the shape of a rectangular prism has a length of 3 5/8 inches, a width of 2 1/2 inches, and a height of 4 inches. What is the volume of the box?
The volume of the rectangular box is equal to 36 1/4 or 36.25 cubic inches.
How to calculate the volume of a rectangular prism?Mathematically, the volume of a rectangular prism can be calculated by using this formula:
Volume = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.Substituting the given parameters into the formula for the volume of a rectangular prism, we have;
Volume of rectangular prism = 3 5/8 × 2 1/2 × 4
Volume of rectangular prism = 29/8 × 5/2 × 4
Volume of rectangular prism = 580/16
Volume of rectangular prism = 36 1/4 or 36.25 cubic inches.
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What is the inverse of negative 10?
Answer: 10. Inverse means opposite so whatever the number is make it the opposite.
Step-by-step explanation:
Ex. opposite of 14 is -14
Function w gives the weight of a cat, in kilograms, when it is m months old. Which statement represents the meaning of the equation w(7)=4 in this situation? Select the correct choice. A The cat weighs 7 kilograms when it is 4 months old.The cat weighs 7 kilograms when it is 4 months old. B The cat weighs 4 kilograms when it is 7 months old.The cat weighs 4 kilograms when it is 7 months old. C The weight of the cat has been 7 kilograms for 4 months.The weight of the cat has been 7 kilograms for 4 months. D The cat weighs 4 kilograms when it is 7 years old.The cat weighs 4 kilograms when it is 7 years old.
Option B) The cat weighs 4 kilograms when it is 7 months old. is the correct answer.
What is Function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given, w gives the weight of the cat, in kgs, when it is "m" months old.
Since w gives weight in kilograms. It outputs weight when we tell the age in months,
thus,
w(7) means weight when the cat is 7 months old.
and w(7) = 4 represents that the cat weighs 4 kilograms when the age of the cat is 7 months.
Therefore, Option B) At 7 months old, the cat weighs 4 kg. is the right response.
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What is the domain of f x )= x 3?
The domain of the function f(x) = x³ is all real numbers
The term domain in function is defined as the set of possible input values and in the graph it consists of all the input values shown on the x-axis.
Here we have the function f(x) = x³.
Now, we have to find the domain of the function.
As per the definition we all know the the set of all x values in the graph is defined as the domain of the function.
As per the given graph we have identified that the domain is all real numbers because the horizontal extent of the graph is the whole real number line.
Here we have also know that the same applies to the vertical extent of the graph, so the domain and range include all real numbers.
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Find the integer a such that
a) a ≡ 43 (mod 23) and −22 ≤ a ≤ 0.
b) a ≡ 17 (mod 29) and −14 ≤ a ≤ 14.
c) a ≡ −11 (mod 21) and 90 ≤ a ≤ 110
a) To find the integer a such that a ≡ 43 (mod 23) and −22 ≤ a ≤ 0, we can use the following steps:
Start with the given congruence: a ≡ 43 (mod 23)Add or subtract multiples of 23 to an until the value of a is between -22 and 0.The smallest such value of a that satisfies the given congruence and the inequality is a = 20b) To find the integer a such that a ≡ 17 (mod 29) and −14 ≤ a ≤ 14, we can use the following steps:
Start with the given congruence: a ≡ 17 (mod 29)Add or subtract multiples of 29 to an until the value of a is between -14 and 14.The smallest such value of a that satisfies the given congruence and the inequality is a = -12c) To find the integer a such that a ≡ −11 (mod 21) and 90 ≤ a ≤ 110, we can use the following steps:
Start with the given congruence: a ≡ −11 (mod 21)Add or subtract multiples of 21 to an until the value of a is between 90 and 110.The smallest such value of a that satisfies the given congruence and the inequality is a = 101It is important to notice that a,b, and c are unique solutions, which means there isn't another solution that satisfies the condition.
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How to do factored form in math?
The term factored form is an algebraic expression with the product of its factors
Here we need to define the factored form in math.
The factored form in math is known as the process of expressing a given number or algebraic expression as the product of its factors is called factoring.
The following three ways are used to convert any quadratic expression into factored form, that is
1) Finding GCD
2) Use identify that is a² - b²
3) Using the identity (x + a) (x + b).
Basically the factored form of a quadratic equations are very helpful in finding its roots or solutions.
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What are the 45 formulas of trigonometry?
There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions.
The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.
By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:
sin θ = Opposite Side/Hypotenuse
cos θ = Adjacent Side/Hypotenuse
tan θ = Opposite Side/Adjacent Side
sec θ = Hypotenuse/Adjacent Side
cosec θ = Hypotenuse/Opposite Side
cot θ = Adjacent Side/Opposite Side
sin 45= 1/√2
cos 45 = 1/√2
sec 45 = 1
cosec45 = 1
tan 45 = √2
cot 45 = √2
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