The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The expression is given below.
⇒ 2(a -3) + 4a
Simplify the expression, then we have
⇒ 2(a -3) + 4a
⇒ 2a - 6 + 4a
⇒ 6a - 6
The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
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The missing options are given below.
A. 6a - 6
B. 6a - 1
C. a - 6
D. None of the above
Δ′ABC ∼Δ′A'B'C and AC=20cm A'C'=15cm B'C'=12cm and A'B'=9cm find the length of the other sides of ΔABC
The length of the other sides of ΔABC are AB =12 cm and BC = 16 cm.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, ΔABC ∼ΔA'B'C' and AC=20 cm A'C'=15 cm B'C'=12 cm and A'B'=9 cm.
Here, AB/A'B' = BC/B'C' = AC/A'C'
AB/9 = BC/12 = 20/15
AB/9 = BC/12 = 4/3
Now, AB/9 = 4/3
AB =12 cm
BC/12 = 4/3
BC = 16 cm
Therefore, the length of AB =12 cm and BC = 16 cm.
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Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.
The common region to both the graphs represents the solution set of the given inequalities.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.
Assume that you worked {x} hours Mowing lawns and {y} hours babysitting.
We can write the inequalities as -
x + y ≤ 15
3x + 5y ≥ 60
Refer to the graph attached. The common region to both the graphs represents the solution set.
Therefore, the common region to both the graphs represents the solution set of the given inequalities.
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recent report suggests the proportion of general us population who believe in extraterrestrial life is 0.47. choose the appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life in greater than the general population?
The null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population
The appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life is greater than the general population can be expressed as follows:
Null hypothesis: The proportion of college students who believe in extraterrestrial life is equal to or less than the general population, or
H0: p <= 0.47
Alternative hypothesis: The proportion of college students who believe in extraterrestrial life is greater than the general population, or
Ha: p > 0.47
where p is the true proportion of college students who believe in extraterrestrial life.
In other words, the null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population (i.e., there is no difference between the two populations), while the alternative hypothesis assumes that the proportion of college students who believe in extraterrestrial life is higher than the general population.
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12. Angle of a right-angled isosceles triangle is:
a. 1 : 2 : 3
b. 1 : 1 : 2
c. 1 : 3 : 4
d. 2 : 2 : 3
A student received a coupon for 43% off the total purchase price at a clothing store. Let b be the original price of the
purchase. Use the expression below for the new price of the purchase. Write an equivalent expression by combining like
terms.
b-0.43b
b-0.43b =
The equivalent expression by combining like terms is 0.57b
How to write an equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
In order to write an equivalent expression by combining like terms, subtract 0.43b from b (Note: b = 1b). That is:
b-0.43b = 0.57b
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Use division to find which of the following fractions are equivalent to
6
24
? Select all that apply.
Answer: C and D are the correct ones
Step-by-step explanation:
8-12
find the missing measures if they are all parallelograms
Answer: Parallelogram angles add up to 360, so use angle properties and known measures.
Step-by-step explanation:
Here are 2 points in the plane.
B
Explain how to construct a line segment that is half the length
of segment AB .
O Construct a new point and create an angle bisector.
Create two circles centered at each point to the other and make a line through their intersections to
cut it in half.
O
Link them with a segment, make a new point on it and make a circle centered at A and B to the new
point.
To construct a line segment that is half the length of segment AB, follow the steps below.
What is the intersection points of the circle?
The intersections of two circles determine a line known as the radical line. If three circles mutually intersect in a single point, their point of intersection is the intersection of their pairwise radical lines, known as the radical center.
Draw a straight line passing through points A and B.
Bisect the line segment AB at point C.
Draw a circle centered at point C with a radius equal to AC or BC.
The intersection points of the circle and the line passing through A and B will be points D and E.
The line segment DE will be half the length of segment AB.
Therefore, To construct a line segment that is half the length of segment AB, follow the steps above.
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Aaron made a picture frame with the dimensions shown in the figure. What is the area of the picture frame? A bigger outer rectangle has sides of 12 cm and 10 cm, and an inner rectangle has sides of 8 cm and 6 cm. A. 120 square centimeters B. 88 square centimeters C. 72 square centimeters D. 64 square centimeters
The area of the picture frame 72 cm². Therefore, option C is the correct answer.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Given that, a bigger outer rectangle has sides of 12 cm and 10 cm.
So, the area of a outer rectangle = 12×10
= 120 cm²
An inner rectangle has sides of 8 cm and 6 cm
The area of a inner rectangle = 8×6
= 48 cm²
The area of the picture frame = 120-48
= 72 cm²
Therefore, option C is the correct answer.
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Answer: C | 72 square centimeters
Step-by-step explanation:
The answer is C. 72 square centimeters. The area of the picture frame can be found by subtracting the area of the inner rectangle from the area of the outer rectangle. The area of the outer rectangle is 120 square centimeters (12 x 10). The area of the inner rectangle is 48 square centimeters (8 x 6). Therefore, the area of the picture frame is 120 - 48 = 72 square centimeters.
jim's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs jim per pound, and type b coffee costs per pound. this month's blend used three times as many pounds of type b coffee as type a, for a total cost of . how many pounds of type a coffee were used?
Type A: 5.45 per pound, Type B: 4.35 per pound. This month's mixture: We know that an is 5.45 per pound, so we divide total cost 401.65 by 5.45 to get a result of 73.69 LB of Type A. 2B + A = 410.35 2(4.35) = 8.70 A + 8.70 = 410.35 A = 401.65.
Total cost is a term used in economics to describe the least expensive way to produce a specific amount of a good (TC). Fixed costs, which are unaffected by the quantity of a good produced and include inputs like buildings and machinery, possibly including sunk costs, and variable costs, which change with the quantity of a good produced and include inputs like labor and raw materials, make up the total economic cost of production. Economics considers the total potential cost of each manufacturing item as one of the total cost's fixed or variable costs.
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17. A class has 20 students. In how many different ways can five students form a group? (Assume
that the order of the students is not important)
Answer: The number of ways to form a group of 5 students from a class of 20 students is calculated using the combination formula:
C(20,5) = 20! / (5! * (20-5)!) = 15504
So, there are 15,504 different ways in which 5 students can form a group.
Step-by-step explanation:
Which equations are true for the values of x, y, and z? Select three options.
2 lines intersect to form 4 angles. Clockwise, from top, the angles are: 65 degrees, x, y, z.
Answer:
Step-by-step explanation:
Based on the information provided, the following three equations are true for the values of x, y, and z:
x + y + z = 360 degrees (Since the sum of the angles in a quadrilateral must equal 360 degrees)
x = 65 degrees (As given, the first angle is 65 degrees)
y + z = 295 degrees (From equation 1, 360 - 65 = 295)
So, the values of x, y, and z can be calculated as 65 degrees, 115 degrees, and 180 degrees respectively.
On a cold day the temperature at Thabana was 6 degres it dropped by 7 degres during the night how many degres will the night temperature be?
Answer:
Step-by-step explanation: The temperature at Thabana dropped by 7 degrees, so we can calculate the night temperature by subtracting 7 from the original temperature of 6 degrees:
Step 1: Subtract 7 from 6:
6 - 7 = -1
Step 2: The night temperature will be -1 degrees.
Mackenzie's company reimburses her $0. 75 per mile that she drives for business. If she goes on a business trip and drives a total of 982 miles, how much will her reimbursement be?
Mackenzie's reimbursement for a business trip would be $736.50 per mile when she drives of a total of 982 miles with $0. 75 per mile.
Mackenzie's reimbursement for driving 982 miles for business can be calculated by multiplying the number of miles driven by the reimbursement rate per mile.
Mackenzie's company reimburses her $0. 75 per mile which is rate per mile.
Reimbursement = miles driven x rate per mile
Filling the value in above equation.
So,
Reimbursement = 982 miles x $0.75/mile
Reimbursement = $736.50
Therefore, Mackenzie's reimbursement for driving 982 miles with the rate of $0. 75 per mile for business would be $736.50.
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Caride Pls this is needed very urgently
1.) Common ailments of senior citizens are arthritis, arteriosclerosis and loss of hearing. A survey of 200 senior citizens found that 70 had arthritis, 60 had arteriosclerosis, 80 had loss of hearing, 35 had arthritis and arteriosclerosis, 33 had arthritis and loss of hearing, 31 had arteriosclerosis and loss of hearing and 15 had all three.
How many of the senior citizens in the survey had; (1). none of these ailments, (f), arthritis but neither of the other two ailments, (iii), exactly one of these ailments, (iv). arteriosclerosis and loss of hearing but not arthritis, (v). arteriosclerosis or loss of hearing but not arthritis, (vi). exactly two of these ailments?
Answer:
i) 84
ii) 7
iii) 47
iv) 16
v) 56
vi) 54
Step-by-step explanation:
The easiest way to understand this problem visually is to create a Venn diagram (See attached diagrams below to help you)
First, note that the total amount of people with each condition beside the relevant circle. Then, since 15 have all 3, write 15 in the center.
We're told 35 had arthritis and arteriosclerosis, and 15 had all 3, so the amount with arthritis and arteriosclerosis only is 25-25=20. So we write 20 in the crosssection between arthritis and arteriosclerosis that doesn't include loss of hearing.
We're told 33 had arthritis and loss of hearing, and 15 had all 3, so the amount with arthritis and loss of hearing but not arteriosclerosis is 33-15=18. So we write 18 in the crosssection between arthritis and loss of hearing that doesn't include arteriosclerosis.
We're told 31 had arteriosclerosis and loss of hearing, and 15 had all 3, so the amount with arteriosclerosis and loss of hearing only is 31-15=16. So we write 16 in the crosssection between arteriosclerosis and loss of hearing that doesn't include arthritis.
(see diagram A to see how this should look)
70 people have arthritis and (18+25+20=63) have arthritis and another condition, so the amount with only arthritis is 70-63=7
60 people have arteriosclerosis and (20+15+16=51) have arteriosclerosis and another condition, so the amount with only arteriosclerosis is 60-51=9
80 people have loss of hearing and (18+15+16=49) have loss of hearing and another condition, so the amount with only loss of hearing is 80-49=31
Marking in these figures completes the diagram (See diagram B to see how it should look)
i)
The total amount of people represented within the diagram (ie, the ones with conditions) is 7+20+9+18+15+16+31=116. If 200 were surveyed, this means the amount without these conditions is 200-116=84
ii)
Above, we found the amount with arthritis only was 7
iii)
7 have only arthrits, 9 have only arteriosclerosis, and 31 have only loss of hearing , so the amount with only one ailment is 7+9+31=47
iv)
Above, we found that 16 had arteriosclerosis and loss of hearing but not arthritis
v)
The amount with arteriosclerosis or loss of hearing but not arthritis is equal to the amount with arteriosclerosis only plus the amount with loss of hearing plus the amount with both arteriosclerosis and loss of hearing: 9+31+16=56
vi)
Above, we found the amount with arthritis and arteriosclerosis only is 20, the amount with arthritis and loss of hearing but not arteriosclerosis is 18, and the amount with amount with arteriosclerosis and loss of hearing only is 16. So the total amount with exactly two conditions is 20+18+16=54
Do the points in the following set lie on the same line? (1,3) (4,2) (-2,4) Explain. Does the point (2, 3) lie on the graph of y = 3x - 4? explain
The slope between the points is same, hence the points lie on the same line. The point (2, 3) does not lie on the graph of y = 3x - 4.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The given points are, (1,3) (4,2) (-2,4):
Calculate the slope of the line formed by the points.
The slope of the line is given by:
m = (y2 - y1)/(x2 - x1)
For (1,3) (4,2):
m = (2 - 3) / (4 - 1) = -1/3
For (4,2) (-2,4):
m = (4 - 2) / (-2 - 4) = 2/ -6 = -1/3
The slope between the points is same, hence the points lie on the same line.
The equation of the graph is:
y = 3x - 4
The given point is (2, 3):
Substituting the point in the equation:
3 = 3(2) - 4
3 = 6 - 4
3 = 2
False.
Hence, the point (2, 3) does not lie on the graph of y = 3x - 4.
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A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length, in feet, of the mat. Then find the area, in square feet, of the mat.
Answer:
length = 12 feet , area = 72 ft²
Step-by-step explanation:
the perimeter (P) is the sum of the 4 sides of the rectangle.
let w be width then length is 2w
opposite sides of a rectangle are congruent , so
P = 2(2w) + 2w = 4w + 2w = 6w
given P = 36 , then
6w = 36 ( divide both sides by 6 )
w = 6
then
length = 2w = 2 × 6 = 12 feet
the area (A) of a rectangle is calculated as
A = length × width = 12 × 6 = 72 ft²
What is the y-intercept of the line shown? (4 points)
A coordinate plane is shown. A line passes through the point -4 comma 1 and through the y-axis at 4.
3 over 4.
2
3
4
Answer:
y- intercept = 4
Step-by-step explanation:
the y- intercept is the value of y on the y- axis where the line crosses.
the line crosses the y- axis at 4
then y- intercept = 4
17) On paper, graph the ordered pairs and label the points. Connect the points in order from A through D with
line segments. (a) What type of quadrilateral is formed? (b) What is the area of the quadrilateral?
A(-2,-1), B(7,-1), C(3,5), D(-2,5)
According to the information, the area of this quadrilateral, trapezoid is 42 cm.
How to calculate the area of this figure?To calculate the area of the figure we must first graph it. Once we have found its shape we must identify what type of quadrilateral it is, in this case we can affirm that it is a right trapezoid.
On the other hand, to calculate its area we must divide the figure in two, one part would be the quadrilateral and the other the triangle. So we need to find the area of both shapes and then add them.
6*5 = 306*4=2424 / 2 = 1212 + 30 = 42So the total area would be 42cm²
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The area of a rectangular window is 4234 cm².
If the length of the window is 73 cm, what is its width?
Answer:
58
Step-by-step explanation:
4234 = 73x divide by 73 on both sides and x=58
A rectangular piece of Bluestone measures 18" on the two long sides and 12" on
the two short sides. To determine the perimeter (or length around the outside), you
add the lengths of the four sides. What is the perimeter of the plate?
The perimeter of the plate is 60"
How to determine the perimeter of the plate?From the question, we have the following parameters that can be used in our computation:
Length = 18"
Width = 12"
The perimeter of the rectangle piece can be calculated as
Perimeter = 2 * (Length + Width)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (18 + 12)
Evaluate
Perimeter = 60
Hence, the perimeyer is 60"
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Select the correct choices to complete the sentence.
In the figure, line m is parallel to line n. Classify the relationship between ∠2 and ∠7 as alternate interior, alternate exterior, or corresponding.
The solution is Option B.
The angles ∠2 and ∠7 are alternate exterior angles
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the parallel lines be represented as m and n
Now , the transversal line is t
The angles formed on line m is ∠1 , ∠2 , ∠3 and ∠4
And , the angles formed on line n is ∠5 , ∠6 , ∠7 and ∠8
Now , the angles ∠2 and ∠7 are situated outside or exterior and is represented by alternate exterior angles
So , pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Hence , the angles are alternate exterior angles
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Diego’s history teacher writes a test for the class with 30 problems. The test is worth 50 points and has two types of problems: multiple choice worth 1 point each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning
By using a system of equations of two variables the number of short answer problems is 10.
Total number of problems in the Test = 30
Maximum points of test = 50
Point of multiple choice = 1
Point of short answer problems = 3
Let the number of multiple choice questions is x and the number of short answer problems is y
So, x + y = 30 - (1)
and 1.x + 3.y = 50 ⇒ x + 3y = 50 -(2)
Equation (2) - Equation (1)
x + 3y - (x + y) = 50 - 30
2y = 20
y = 10
Put y = 10 in equation (1)
x = 30 - 10 = 20
Hence, the number of multiple-choice questions = 20 and the number of short answer problems = 10.
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HI PLEASE HELP NEED ANSWERS ASAP :(!!
Question 7(Multiple Choice Worth 2 points) (09.06 LC) How many hectometers are in 580 millimeters? O 0.0058 hectometers O 0.058 hectometers O 58,000 hectometers O 580,000 hectometers
Answer:
0.058 hectometers
Step-by-step explanation:
There are 0.058 hectometers in 580 millimeters.
To convert millimeters to hectometers, you need to divide the number of millimeters by 100,000. So, 580 millimeters divided by 100,000 equals 0.0058 hectometers, or 0.058 hectometers when rounded to two decimal places.
A rectangle has a length of ( + ) and a width of ( − ). Determine the expression that represents the area of this rectangle.
Answer:
Step-by-step explanation:
The expression that represents the area of a rectangle with length (l) and width (w) is given by:
A = l * w
Therefore, the expression that represents the area of a rectangle with a length of ( + ) and a width of ( − ) can be represented as:
A = ( + ) * ( − ) = + × − = + (−) = −.
1. If you roll a single die and get 4 fives in a row, what is the probability that you'll get a five on the
next roll?
2. What is the probability that you'll get 5 fives in a row when rolling a single die?
3. A roulette wheel has 38 numbers. If the "lucky" number 7 comes up twice in a row, what is the
probability it will come up on the very next roll?
4. What is the probability of getting three 7's in a row on a roulette wheel?
5. If I type randint(1,10) on my calculator, I get a random integer between 1 and 10 (inclusive). If I
do this 6 times, what is the probability that all 6 outcomes will be a 1?
6. If I roll a pair of dice, what is the probability of getting a pair of sixes?
7. If I roll a pair of dice, what is the probability of getting any pair?
1. 1/6 is the probability of rolling a five on the next roll.
2. The probability of getting 5 fives in a row when rolling a single die is 1/7776 .
3. 1/38 is he probability of 7 coming up on the very next spin is
4. 1/54782 is the probability of getting three 7's in a row on a roulette wheel.
5. (1/10)⁶ is the probability of getting a 1 on all six trials.
6. 1/36 is the probability of getting a pair of sixes when rolling a pair of dice is
7. The probability of getting any pair is 1/6
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
1. The probability of rolling a five on a single roll of a fair die is 1/6, since there are six equally likely outcomes: rolling a 1, 2, 3, 4, 5, or 6.
the probability of rolling a five on the next roll is still 1/6, regardless of whether the previous rolls resulted in four fives in a row or not.
2. The probability of getting a five on a single roll of a fair die is 1/6, as there are six equally likely outcomes.
the probability of getting 5 fives in a row when rolling a single die is:
(1/6) × (1/6) × (1/6) × (1/6) × (1/6) = 1/7776
3. The probability of any particular number coming up on a single spin of an American roulette wheel with 38 numbers is 1/38, since there are 38 equally likely outcomes.
As these are independent , the probability of 7 coming up on the very next spin is still 1/38.
4. The probability of getting three 7's in a row on a roulette wheel is:
(1/38) × (1/38) × (1/38) = 1/54,872
5. The probability of generating a 1 on a single trial is 1/10.
The probability of getting a 1 on a single trial by itself six times
(1/10) × (1/10) × (1/10) × (1/10) × (1/10) × (1/10) = (1/10)⁶
The probability of getting a 1 on all six trials is (1/10)⁶
6.
The probability of getting a pair of sixes when rolling a pair of dice is:
1/36
7.
The probability of getting any pair when rolling a pair of dice is:
Number of ways to get a pair / Total number of possible outcomes
= 6 / 36
= 1 / 6
So the probability of getting any pair is 1/6
Hence,
1. The probability of rolling a five on the next roll is 1/6.
2. 1/7776 is the probability of getting 5 fives in a row when rolling a single die.
3. The probability of 7 coming up on the very next spin is 1/38.
4. The probability of getting three 7's in a row on a roulette wheel is 1/54782
5. The probability of getting a 1 on all six trials is (1/10)⁶
6. The probability of getting a pair of sixes when rolling a pair of dice is:
1/36
7. the probability of getting any pair is 1/6
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1. Dante mixes 30 milliliters of one liquid with 2 centiliters of a second
liquid. How many centiliters of liquid does he have altogether?
A. 5 cL
B. 32 cL
C. 50 CL
D. 302 CL
The total volume in centiliters is 5 cL, then the correct option is A.
How many centiliters of liquid does he have altogether?Here we know that Dante mixes 30 mililiters of one liquid with 2 centiliters of a second liquid, and we want to find the total volume in centiiters.
We know that:
1 milliliter = 0.1 centiliters.
Then:
30 mililiters = 30*( 0.1 centiliters) = 3 centilters.
Then the sum of the two volumes is:
3 centiliters + 2 centiliters = 5 centiliters.
Then the correct option is A.
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The answer is A. 5 cL.
What is liquid?Liquid is one of the three states of matter, alongside solid and gas. It is a form of matter that has a definite volume, but not a definite shape. Liquids take the shape of their container and are able to flow and be poured.
First, we need to convert 30 milliliters to centiliters, which is 3 centiliters (since 1 centiliter = 10 milliliters).
Then, we can add the 3 centiliters to the 2 centiliters of the second liquid to get a total of 5 centiliters.
Therefore, the answer is A. 5 cL.
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1000, 200, 40, .... Find the 50th term:
PLEASE GIVE BRAINLIEST
thank you and have a good day :)
Answer:
5.6294995342131E-32
Step-by-step explanation:
the common ratio is 1/5, therefore with the equation an = a x r
n-1
we can figure out the answer to this by plugging in the common ratio for r,
and n as the number in the sequence that we want to obtain.
a is simply the first number (1000)
In the rectangle ABCD given in the figure, AB = 3x + 2 cm and AD=x+3 cm. It is given that APQD is a square. Show that PB=2x-1 cm and It is given that AB/AD=PQ/PB Show that 5x²-5x-11-0.
Answer:
no answer
soory
Step-by-step explanation:
