How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) – 2
1 answer:
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The total monthly bill of the gym = $53
The cost of membership of a month = $25
Let 'n' be extra the number of hours Bella worked on.
The cost for working on extra hours = $4
So, we have to determine the equation, Bella worked out after hours.
We will determine the equation by:
(Monthly cost of membership) + ( cost for extra hours number of hours extra worked on ) = Total monthly bill received
So, we get
$25+4n = $53 is the required equation.
Therefore, $25+4n = $53 equation can be used to determine how many times Bella worked out after hours.
Answer: The correct option is
(A) The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.
Step-by-step explanation: We are given to select the correct condition that might be true if polygons ABCD and KLMN are similar.
Two polygons are said to be SIMILAR if corresponding angles are congruent and corresponding sides are proportional.
So, options (B), (C), (D) and (E) are not correct because they contradict conditions of similarity.
In option (A), we have
The measures of corresponding angles of ABCD and KLMN are equal. So, they must be congruent.
And the lengths of corresponding sides of ABCD are half those of KLMN.
So, we can write
Therefore, the corresponding sides are proportional.
Thus, option (A) is true if two polygons are similar.
Answer:
Due to the higher z-score, David has the higher standardized score
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Which student has the higher standardized score
Whoever had the higher z-score.
David:
Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. So
Steven:
Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. So
Due to the higher z-score, David has the higher standardized score
The picture in the attached figure
we know that
area of a sector=(∅*pi/360°)*r²--------> when ∅ is in degree
in this problem
∅=120°
r=4 units
so
area of a sector=(120°*pi/360°)*4²-------> (120°/360°)*(16*pi) units²
The <span>expressions to find the area of the shaded sector is
</span>(120°/360°)*(16*pi) units²
(1/3)*(16*pi)----> (16/3)*pi units²
the area of the shaded sector is (16/3)*pi units²
we know that
area of a sector=(∅*pi/360°)*r²--------> when ∅ is in degree
in this problem
∅=120°
r=4 units
so
area of a sector=(120°*pi/360°)*4²-------> (120°/360°)*(16*pi) units²
The <span>expressions to find the area of the shaded sector is
</span>(120°/360°)*(16*pi) units²
(1/3)*(16*pi)----> (16/3)*pi units²
the area of the shaded sector is (16/3)*pi units²